Index: src/wp-admin/includes/ajax-actions.php
IDEA additional info:
Subsystem: com.intellij.openapi.diff.impl.patch.CharsetEP
<+>UTF-8
===================================================================
--- src/wp-admin/includes/ajax-actions.php	(date 1512512466000)
+++ src/wp-admin/includes/ajax-actions.php	(date 1512681020000)
@@ -4105,8 +4105,8 @@
 		'newVersion' => '',
 	);
 
-	if ( ! current_user_can( 'update_plugins' ) || 0 !== validate_file( $plugin ) ) {
-		$status['errorMessage'] = __( 'Sorry, you are not allowed to update plugins for this site.' );
+	if ( ! current_user_can( 'update_plugin', $plugin ) || 0 !== validate_file( $plugin ) ) {
+		$status['errorMessage'] = __( 'Sorry, you are not allowed to update this plugin.' );
 		wp_send_json_error( $status );
 	}
 
Index: src/wp-admin/includes/plugin-install.php
IDEA additional info:
Subsystem: com.intellij.openapi.diff.impl.patch.CharsetEP
<+>UTF-8
===================================================================
--- src/wp-admin/includes/plugin-install.php	(date 1512512466000)
+++ src/wp-admin/includes/plugin-install.php	(date 1512681020000)
@@ -420,7 +420,7 @@
 				$status      = 'update_available';
 				$update_file = $file;
 				$version     = $plugin->new_version;
-				if ( current_user_can( 'update_plugins' ) ) {
+				if ( current_user_can( 'update_plugin', $file ) ) {
 					$url = wp_nonce_url( self_admin_url( 'update.php?action=upgrade-plugin&plugin=' . $update_file ), 'upgrade-plugin_' . $update_file );
 				}
 				break;
Index: src/wp-admin/includes/update.php
IDEA additional info:
Subsystem: com.intellij.openapi.diff.impl.patch.CharsetEP
<+>UTF-8
===================================================================
--- src/wp-admin/includes/update.php	(date 1512512466000)
+++ src/wp-admin/includes/update.php	(date 1512681020000)
@@ -344,6 +344,26 @@
 	return $upgrade_plugins;
 }
 
+/**
+ * Returns the number of plugins that the current user isn't allowed to update
+ *
+ * @return int
+ */
+function wp_get_plugin_updates_disallowed_count() {
+
+	// The number of plugins that current user cannot update
+	$not_allowed_to_update_count = 0;
+
+	$all_plugins = get_plugins();
+	foreach ( (array) $all_plugins as $plugin_file => $plugin_data ) {
+		if ( ! current_user_can( 'update_plugin', $plugin_file ) ) {
+			$not_allowed_to_update_count++;
+		}
+	}
+
+	return $not_allowed_to_update_count;
+}
+
 /**
  * @since 2.9.0
  */
@@ -403,7 +423,7 @@
 
 		echo '<tr class="plugin-update-tr' . $active_class . '" id="' . esc_attr( $response->slug . '-update' ) . '" data-slug="' . esc_attr( $response->slug ) . '" data-plugin="' . esc_attr( $file ) . '"><td colspan="' . esc_attr( $wp_list_table->get_column_count() ) . '" class="plugin-update colspanchange"><div class="update-message notice inline notice-warning notice-alt"><p>';
 
-		if ( ! current_user_can( 'update_plugins' ) ) {
+		if ( ! current_user_can( 'update_plugin', $file ) ) {
 			/* translators: 1: plugin name, 2: details URL, 3: additional link attributes, 4: version number */
 			printf(
 				__( 'There is a new version of %1$s available. <a href="%2$s" %3$s>View version %4$s details</a>.' ),
Index: src/wp-admin/plugin-editor.php
IDEA additional info:
Subsystem: com.intellij.openapi.diff.impl.patch.CharsetEP
<+>UTF-8
===================================================================
--- src/wp-admin/plugin-editor.php	(date 1512512466000)
+++ src/wp-admin/plugin-editor.php	(date 1512681020000)
@@ -18,7 +18,7 @@
 $plugin = isset( $_REQUEST['plugin'] ) ? wp_unslash( sanitize_text_field( $_REQUEST['plugin'] ) ) : '';
 
 if ( ! current_user_can( 'edit_plugin', $plugin) ) {
-    if( empty( $plugin ) )
+    if ( empty( $plugin ) )
 	    wp_die( __( 'Sorry, you are not allowed to edit plugins for this site.' ) );
     else
 	    wp_die( __( 'Sorry, you are not allowed to edit this plugin.' ) );
@@ -216,7 +216,7 @@
 <?php
 foreach ( $plugins as $plugin_key => $a_plugin ) {
 
-    if( ! current_user_can( 'edit_plugin', $plugin_key) )
+    if ( ! current_user_can( 'edit_plugin', $plugin_key) )
         continue;
 
 	$plugin_name = $a_plugin['Name'];
Index: src/wp-admin/update-core.php
IDEA additional info:
Subsystem: com.intellij.openapi.diff.impl.patch.CharsetEP
<+>UTF-8
===================================================================
--- src/wp-admin/update-core.php	(date 1512512466000)
+++ src/wp-admin/update-core.php	(date 1512681020000)
@@ -233,9 +233,11 @@
 
 	require_once( ABSPATH . 'wp-admin/includes/plugin-install.php' );
 	$plugins = get_plugin_updates();
-	if ( empty( $plugins ) ) {
+
+	// If all plugins are up to date or the only plugins to update cannot be update by the current user
+	if ( empty( $plugins ) || count( $plugins ) == wp_get_plugin_updates_disallowed_count()) {
 		echo '<h2>' . __( 'Plugins' ) . '</h2>';
-		echo '<p>' . __( 'Your plugins are all up to date.' ) . '</p>';
+		echo '<p>' . __( "There isn't any plugin to update." ) . '</p>';
 		return;
 	}
 	$form_action = 'update-core.php?action=do-plugin-upgrade';
@@ -263,6 +265,10 @@
 	<tbody class="plugins">
 <?php
 foreach ( (array) $plugins as $plugin_file => $plugin_data ) {
+
+    if ( ! current_user_can( 'update_plugin', $plugin_file) )
+        continue;
+
 	$plugin_data = (object) _get_plugin_data_markup_translate( $plugin_file, (array) $plugin_data, false, true );
 
 	$icon            = '<span class="dashicons dashicons-admin-plugins"></span>';
@@ -719,7 +725,7 @@
 } elseif ( 'do-plugin-upgrade' == $action ) {
 
 	if ( ! current_user_can( 'update_plugins' ) ) {
-		wp_die( __( 'Sorry, you are not allowed to update this site.' ) );
+		wp_die( __( 'Sorry, you are not allowed to update plugins for this site.' ) );
 	}
 
 	check_admin_referer( 'upgrade-core' );
Index: src/wp-admin/update.php
IDEA additional info:
Subsystem: com.intellij.openapi.diff.impl.patch.CharsetEP
<+>UTF-8
===================================================================
--- src/wp-admin/update.php	(date 1512512466000)
+++ src/wp-admin/update.php	(date 1512681020000)
@@ -35,6 +35,14 @@
 			$plugins = array();
 		}
 
+		foreach ( $plugins as $plugin_file ) {
+			if ( ! current_user_can( 'update_plugin', $plugin_file ) ) {
+				if ( ( $key = array_search( $plugin_file, $plugins ) ) !== false ) {
+					unset( $plugins[ $key ] );
+				}
+			}
+		}
+
 		$plugins = array_map( 'urldecode', $plugins );
 
 		$url   = 'update.php?action=update-selected&amp;plugins=' . urlencode( implode( ',', $plugins ) );
@@ -49,8 +57,8 @@
 		iframe_footer();
 
 	} elseif ( 'upgrade-plugin' == $action ) {
-		if ( ! current_user_can( 'update_plugins' ) ) {
-			wp_die( __( 'Sorry, you are not allowed to update plugins for this site.' ) );
+		if ( ! current_user_can( 'update_plugin', $plugin ) ) {
+			wp_die( __( 'Sorry, you are not allowed to update this plugin.' ) );
 		}
 
 		check_admin_referer( 'upgrade-plugin_' . $plugin );
@@ -71,8 +79,8 @@
 		include( ABSPATH . 'wp-admin/admin-footer.php' );
 
 	} elseif ( 'activate-plugin' == $action ) {
-		if ( ! current_user_can( 'update_plugins' ) ) {
-			wp_die( __( 'Sorry, you are not allowed to update plugins for this site.' ) );
+		if ( ! current_user_can( 'update_plugin', $plugin ) ) {
+			wp_die( __( 'Sorry, you are not allowed to update this plugin.' ) );
 		}
 
 		check_admin_referer( 'activate-plugin_' . $plugin );
Index: src/wp-includes/capabilities.php
IDEA additional info:
Subsystem: com.intellij.openapi.diff.impl.patch.CharsetEP
<+>UTF-8
===================================================================
--- src/wp-includes/capabilities.php	(date 1512512466000)
+++ src/wp-includes/capabilities.php	(date 1512681020000)
@@ -416,6 +416,7 @@
 			}
 			break;
 		case 'update_plugins':
+		case 'update_plugin':
 		case 'delete_plugins':
 		case 'delete_plugin':
 		case 'install_plugins':
@@ -436,7 +437,13 @@
 			} elseif ( 'upload_plugins' === $cap ) {
 				$caps[] = 'install_plugins';
 			} else {
-				$caps[] = ( $cap == 'delete_plugin' ) ? 'delete_plugins' : $cap;
+
+				if (  $cap == 'delete_plugin' )
+					$caps[] = 'delete_plugins';
+				elseif (  $cap == 'update_plugin' )
+					$caps[] = 'update_plugins';
+				else
+					$caps[] = $cap;
 			}
 			break;
 		case 'install_languages':
Index: src/wp-includes/update.php
IDEA additional info:
Subsystem: com.intellij.openapi.diff.impl.patch.CharsetEP
<+>UTF-8
===================================================================
--- src/wp-includes/update.php	(date 1512512466000)
+++ src/wp-includes/update.php	(date 1512681020000)
@@ -636,7 +636,7 @@
 	if ( $plugins = current_user_can( 'update_plugins' ) ) {
 		$update_plugins = get_site_transient( 'update_plugins' );
 		if ( ! empty( $update_plugins->response ) ) {
-			$counts['plugins'] = count( $update_plugins->response );
+			$counts['plugins'] = count( $update_plugins->response ) - wp_get_plugin_updates_disallowed_count();
 		}
 	}