I was wondering how much of the theory say of Lazarsfeld books can be carried to algebraic stacks (if this has been done).

Do we have a sensible notion of ample (big, nef) line bundle? Of ample vector bundle? How many of the usual results carry over? Do we have multiplier ideal sheaves? Are the usual vanishing theorems valid in this settings? And so on.

I hope the question even makes sense. I am complete beginner with stacks, so it may even turn out that the relevant objects cannot be defined and the question is too naif.