I can read this without the "she kissed someone else" and see a break-up. You are no longer attracted to her in that way.

If you choose to break-up, don't mention cheating or anyone else. Just tell her you are not feeling for her the passion you once did, and you feel the relationship is tired. Would you rather be friends? Can you give her time to move out? The discussion doesn't need to end the living arrangement. You might stay roommates till the end of your current lease (or a month or two after the discussion).