Geodesic
The algebraic analog of the Borel construction and its properties
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 22, Tome 394 (2011), pp. 262-293
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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. 
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I. B. Kobyzev. The algebraic analog of the Borel construction and its properties. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 22, Tome 394 (2011), pp. 262-293. http://geodesic.mathdoc.fr/item/ZNSL_2011_394_a9/

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