The algebraic analog of the Borel construction and its properties

Suppose that $G$ is an affine algebraic group scheme faithfully flat over another affine scheme $X=\operatorname{Spec}R$, $H$ is a closed faithfully flat $X$-subscheme and $G/H$ is an affine $X$-scheme. In this case we prove the equivalence of two categories: left $R[H]$-comodules and $G$-equivariant vector bundles over $G/H$, and that this equivalence respects tensor products. Our algebraic construction is based on the well-known geometric Borel construction.