Equivariant Hartogs: extending $G$-equivariant vector bundle to codimension 2

Question

Let $X$ be a normal variety with an action of $G$ and $X_0 \subset X$ be an open $G$-invariant subset whose complement is of codimension at least 2. Every vector bundle on $X_0$ extends to a vector bundle on $X$ (see this answer, for example). Is the same true for $G$-equivariant vector bundles?

Answer 1

First, you can extend just the vector bundle. Then you should check that the equivariant structure extends. The latter amounts to some morphisms $g^*E \to E$ for $g \in G$, so in the end the question is in extension of functions, which exists by Hartogs.