Hi,

Suppose that $G$ is a group acting on a scheme $X$, and $F$ is an $l$-adic sheaf on $X$ EDIT: with an action of $G$ (thanks Torsten). Is it true that $R\Gamma(X,F)$ is well-defined as an object of the derived category of $G$-equivariant $l$-adic sheaves? I'm thinking about the case when $G$ = Galois group, but I'm also interested in the more general case.

Thanks!