Module Over the Group Algebra of a Ring

Question

I'm aware that if $K$ is a field, $V$ a $K$-vector space, and $G$ is a group, then a $K$-representation of $G$ in $V$ is the same thing as a $KG$-module, where $KG$ is the group algebra of $G$ over $K$. I'm working on an exercise that asks how the situation changes when $K$ is any commutative ring. Would it be true then that a $KG$ module is still the same thing as a group homomorphism $G \to \operatorname{Aut}_K(V,V)$? If so, is there a name for this structure? (I would guess something along the lines of a "module-representation of a group" but after a quick Google search it seems like this isn't a structure that's talked about.)