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Let H be a Hopf algebra over a field k, and let A/B be a Hopf Galois extension. We shall construct a = H/[H, H] comodule structure on the Hochschild homology of A with coefficients in a Hopf bimodule M. Then, for a subcoalgcbra C
, we construct certain functors HC(A, –) from Hopf bimodules to k-spaces and we set up a spectral sequence for describing them
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