Suppose a (linear algebraic) group $G$ acts on a variety $X$ and that $U$ is a $G$-invariant open subvariety. My question is: under what conditions is the restriction functor

$i^*: Vect^G(X) \rightarrow Vect^G(U)$

an equivalence of categories of $G$-equivariant vector bundles? Obviously not in general, but we do have: if $X$ is normal (I think Gorenstein or even less will do actually) and $U$ is dense with complement of codimension at least 2 then $i^*$ is fully faithful. What more is needed to make it surjective? What if the complement of $U$ is actually a fixed point of the $G$ action?

The example I have in my head here is that of $G$ being the product of a finite subgroup of $SL(2,\mathbb{C})$ and a $\mathbb{C}^*$, acting canonically on $X = \mathbb{C}^2$. Then the $G$-equivariant vector bundles on the punctured plane should be equivalent to those on the whole $\mathbb{C}^2$, that is to representations of $G$. So I guess I'm asking: why is this true?