Tensor product via the diagonal action of a Hopf algebra

Question

Let $H$ be a Hopf algebra and $V$ and $W$ two left $H$-modules, then $V\otimes W$ is also a left $H$-module via the comultiplication of $H$. I now want to consider the functor $-\otimes_H (V\otimes W)$. Is there some kind of distributivity law in this situation? If necessary one can specify $H$ to be a group algebra.