Hopf algebra equivariant cyclic theory

This thesis deals with Hopf-algebra equivariant cyclic theory. We consider the cyclic homology of algebras and coalgebras equipped with the action or coaction of a Hopf algebra. Various kinds of equivariant cyclic modules related to Hopf (co)module algebras and Hopf (co)module coalgebras are introduced. We give spectral sequences to compute these equivariant theories and compute the $E0,E1$and $E2$ terms of these spectral sequences. We also link our theory with a Hopf algebra equivariant K-theory.