Coactions on Hochschild homology of Hopf-Galois extensions and their coinvariants

Let B⊆A be an H-Galois extension, where H is a Hopf algebra over a field K. If M is a Hopf bimodule then , the Hochschild homology of A with coefficients in M, is a right comodule over the coalgebra C_H=H/H,H]. Given an injective left C_H-comodule V, our aim is to understand the relationship between and . The roots of this problem can be found in Lorenz (1994) 15], where and are shown to be isomorphic for any centrally G-Galois extension. To approach the above mentioned problem, in the case when A is a faithfully flat B-module and H satisfies some technical conditions, we construct a spectral sequence