Notation for equivariant sheaves

Question

Let $G$ be a finite group acting on a variety $X$, and $F$ an equivariant coherent sheaf on $X$. I have seen the notation $F\otimes\rho$, where $\rho$ is a representation of $G$. What does it stand for? (It is supposed to be another equivariant coherent sheaf.)

Answer 1

You can think of $\rho$ as of an equivariant sheaf on the point $Spec(k)$. Then, if $f \colon X \to Spec(k)$ is the structure morphism then $$ F \otimes \rho = F \otimes f^*(\rho). $$