Group-stack

In algebraic geometry, a group-stack is an algebraic stack whose categories of points have group structures or even groupoid structures in a compatible way. It generalizes a group scheme, which is a scheme whose sets of points have group structures in a compatible way.
Actions of group-stacks.
The definition of a group action of a group-stack is a bit tricky. First, given an algebraic stack "X" and a group scheme "G" on a base scheme "S", a right action of "G" on "X" consists of
that satisfy the typical compatibility conditions.
If, more generally, "G" is a group-stack, one then extends the above using local presentations.