You can set the timeout in web.config under system.web -> sessionState -> timeout. Not sure if you can have an infinite session though.
Also, you might be interested in the Application object which stores things in the "application's session" instead of the user's. Comes to my mind because you speak of a "global" session.
What's the application for this? Sounds like you're actually trying to use the session as a persistent storage, which will however only seemingly work even if you manage to set timeout to never or 5 years or whatever - because sessions will be "timed out" once the application is restarted. You might still get around that, but you might be better off looking for real persistence solution like a database. I may be totally off guessing your application for that of course.