Cup Products in Hopf-Cyclic Cohomology

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We construct cup products of two different kinds for Hopf-cyclic cohomology. When the Hopf algebra reduces to the ground field our first cup product reduces to Connes' cup product in ordinary cyclic cohomology. The second cup product generalizes Connes-Moscovici's characteristic map for actions of Hopf algebras on algebras.
7 pages. To appear in C. R. Acad. Sci. Paris

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