long exact sequence of representations

Question

Let $G$ be a group and $V_1,V_2 $ be $G$-representations. Are the ${\rm Ext}^i(V_1,V_2)$ $G$-representations as well?

Once established this, suppose I have a short exact sequence $$0\to V_1\to V_2\to V_3\to 0$$ is the long exact sequence in cohomology obtained applying ${\rm Hom}(V,-) $ for another $G$-representation $V$ an exact sequence of representations as well?

Answer 1

You can think of $\operatorname{Ext}_G^i(V_1, V_2)$ as a $G$-module with the trivial action (every element of $G$ acts as the identity).