This is mostly a reference question. Suppose that I have an action of (say, finite) group $G$ on an algebraic stack $X$ (in my case it is a Deligne-Mumford stack, but this shouldn't matter). As far as I understand, in this case it makes sense to talk about the fixed points stack $X^G$ (which is not a closed substack of $X$). Does anybody know a good reference for this notion and various things related to it (tangent spaces etc.)?
A standard reference is
Romagny, Matthieu Group actions on stacks and applications. Michigan Math. J. 53 (2005), no. 1, 209–236.