Well, I would 'guess' that you have a loose connection of some sort, possibly in a harness that when pressure is applied to it on left turns, loses contact and then returns to normal when you straighten out. I would say it's related to electrical since the XM, etc also is affected. I know the XM receiver is tied into the starting system on many of these cars. We had one with an intermittent no start that ended up being due to the XM box. I would start the car and while it's running, go around and do a pull test on all the harnesses (gently tug and wiggle on every harness you can reach) Gently banging on the inside panels and console might also reveal a faulty connection as well. If the engine stumbles, stalls or otherwise while you're doing this, you've found the faulty connection.
Then again, there's always taking it to the dealer and letting them diagnose it under warranty (if still under warranty) Fortunately your problem sounds like it's easy to diagnose and will happen every time. Intermittent problems are the hardest to diagnose so consider yourself lucky on this one.
