In the case of movement, I feel the most consistent ruling is a soft one. Through misdirection, or guile, or doing nothing to attract attention to yourself, you are able to move around behind cover and your enemies don't target you. It's not that they couldn't target you if something drew their attention to you, but that nothing draws their attention to you.
So then if one of their buddies goes 'Who's that' pointing you out (his passive Perception beat your Stealth) they can all immediately notice you and even attack you, at -2 and still yielding you CA.
Once you are noticed, any power that explictly grants a check should let you make one. Fleeting Ghost, for instance. Other than that, you should do something cunning that your DM can say 'yes, that works' to. Breaking LOS should in my view nearly always work, including teleporting to a square they aren't looking at (since you don't pass through the intervening space).
-vk