How to correctly specify routes in the pager?

Question

Yii

Hello everyone, I ran into a problem, there is a regular page with pagination

$query = FalseBase::find()->where(['status' => 1])->orderBy(['id' => SORT_DESC]);

        
        $pages = new Pagination([
            'totalCount' => $query->count(), 'pageSize' => 6,
            'forcePageParam' => false, 'pageSizeParam' => false,
            'route' => 'admin/false-filter/index'
        ]);

        
        $falsers = $query->offset($pages->offset)->limit($pages->limit)->all();

        return $this->render('index',compact('falsers','pages'));

And on it there is an AJAX-om removal, when I delete, I return an updated list of data, but from another controller

public function actionDelete($id)
    {

        $model = $this->findModel($id);

        //Если модель удаленна
        if ($model->delete()) {

            //Удалим ее картинки
            $deleter = new ImageDeleter;
            $deleter->deleteImg($id, 'False');
        }

        //Запрос обновленного списка кидал
        $query = FalseBase::find()->with('phones')->with('addresses')->with('photo')->where(['status' => [1,2]])->orderBy(['id' => SORT_DESC]);

        //Пейджер
        $pages = new Pagination([
            'totalCount' => $query->count(), 'pageSize' => 6,
            'forcePageParam' => false, 'pageSizeParam' => false,
            'route' => 'admin/false/index'
        ]);

        $falsers = $query->offset($pages->offset)->limit($pages->limit)->all();


        return $this->renderAjax('index', compact('falsers','pages'));

    }

And if I don’t specify the line 'route' => 'admin/false/index' , the urle remains the wrong thing (Pjax-pagination), and if I specify, then pagination does not work (please help me, I already understand that I didn’t implement it correctly, but how to fix it now?