Usually a web app (MVC or WebForms) isn't the best place to run scheduled tasks. It can be done, but you will get things like IIS recycling application pools and other anomalies, which although useful to a web app, could get in the way of reliably scheduling tasks.
A lot of developers (and my favourite too) schedule their tasks in a Windows Service. This can be installed and can be set to gracefully start and stop when the server starts and shuts down. You can then set up logging and other health monitoring to monitor the state of your scheduler service.
However if your tasks is purely SQL based you may wish to use SQL Server's inbuilt scheduling (or similar for any other database). Another alternative is to use the operating system's scheduler.
Edit
In regard to updating your view with the results, you can store and update the status of your scheduled tasks in the database with columns like 'TaskStatus' (New, Waiting, Running, Aborted, Failed, Cancelled, Completed) and 'TaskResult' (probably empty for success or the error message from a failure). You can then show and filter this information on your results view by retrieving it from the database.