Let $G$ be an algebraic group over an algebraically closed field of characteristic zero $K$ and let $L$ be another algebraically closed field, together with an embedding $K \hookrightarrow L$. 

Why is it true that the extension of scalars is an equivalence of categories from finite dimensional $K$-representations of $G$ to finite-dimensional $L$ representations of $G \times_K L$? 

Are all the assumptions on the fields (algebraically closed, characteristic zero) needed?