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We show that Connes' B-operator on a cyclic differential graded k-module M isa model for the canonical circle action on the geometric realization of M. Thisimplies that the negative cyclic homology and the periodic cyclic homology of adifferential graded category can be identified with the homotopy fixed pointsand the Tate fixed points of the circle action on its Hochschild complex.

The homotopy fixed points of the circle action on Hochschild homology