If the key mechanism on your fuel cap has broken, read this:
https://forums.bmwmoa.org/showthread...Stuck-Fuel-Cap
If you are trying to open a cap that is off the bike (lost key, bought off eBay with no key, lock broke after rebuild but haven't reinstalled, etc.):
Drill a small (1/8" should do) hole at the very front of the filler ring just below the flange. Angle the hole slightly up towards the cap.
DO NOT DRILL ALL THE WAY THROUGH! Stop drilling when you hit the tongue of the latch. The latch is steel, the flange is aluminum.
Just drill a little at a time and check. Use a nail or a punch to push the latch in. Fill with fuel resistant epoxy when done.
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