bp_activity_user_can_delete( false|BP_Activity_Activity $activity = false )

function bp_activity_user_can_delete( $activity = false ) {
	global $activities_template;

	// Try to use current activity if none was passed.
	if ( empty( $activity ) && ! empty( $activities_template->activity ) ) {
		$activity = $activities_template->activity;
	}

	// If current_comment is set, we'll use that in place of the main activity.
	if ( isset( $activity->current_comment ) ) {
		$activity = $activity->current_comment;
	}

	// Assume the user cannot delete the activity item.
	$can_delete = false;

	// Only logged in users can delete activity.
	if ( is_user_logged_in() ) {

		// Community moderators can always delete activity (at least for now).
		if ( bp_current_user_can( 'bp_moderate' ) ) {
			$can_delete = true;
		}

		// Users are allowed to delete their own activity. This is actually
		// quite powerful, because doing so also deletes all comments to that
		// activity item. We should revisit this eventually.
		if ( isset( $activity->user_id ) && ( $activity->user_id === bp_loggedin_user_id() ) ) {
			$can_delete = true;
		}

		// Viewing a single item, and this user is an admin of that item.
		if ( bp_is_single_item() && bp_is_item_admin() ) {
			$can_delete = true;
		}
	}

	/**
	 * Filters whether the current user can delete an activity item.
	 *
	 * @since BuddyPress 1.5.0
	 *
	 * @param bool   $can_delete Whether the user can delete the item.
	 * @param object $activity   Current activity item object.
	 */
	return (bool) apply_filters( 'bp_activity_user_can_delete', $can_delete, $activity );
}