Homology of Epsilon-Strongly Graded Algebras

Let G be a group and S a unital epsilon-strongly G-graded algebra. We construct spectral sequences converging to the Hochschild (co)homology of S. Each spectral sequence is expressed in terms of the partial group (co)homology of G with coefficients in the Hochschild (co)homology of the degree-one component of S. Moreover, we show that the homology spectral sequence decomposes according to the conjugacy classes of G, and, by means of the globalization functor, its E²-page can be identified with the ordinary group homology of suitable centralizers.