Let $X$ be a topological space 
equipped with an action of a group $G$. In the Tohoku paper, Grothendieck defined
"$G$-sheaves" on $X$ as sheaves equipped with $G$-action on the etale space,
compatible with the $G$-action on $X$. It is more or less the same
as $G$-equivariant objects in the category of sheaves on $X$ with respect
to $G$ acting on this category by endofunctors, but the notion of "$G$-equivariant sheaves" is taken over by sheaves equivariant with respect to a group scheme
or to a continuous action of a topological group.

Suppose now
that the action of $G$ on $X$ is free. Then the 
category of $G$-sheaves on $X$ is equivalent to the category
of sheaves on $X/G$. I need this statement when $G$ acts on a manifold $X$ properly
discontinuously, but I suppose this is true in all generality.
I have a proof which works (at least for properly
discontinuous actions), but it's a bit too long for such a 
classical-looking statement, so I am asking for a reference 
I can use for this. I spent quite a few hours googling and browsing the Stacks Project, without avail.