The Structure of the Hopf Cyclic (Co)Homology of Algebras of Smooth Functions

The paper discusses the structure of the Hopf cyclic homology and cohomology of the algebra of smooth functions on a manifold provided that the algebra is endowed with an action or a coaction of the algebra of Hopf functions on a finite or compact group or of the Hopf algebra dual to it. In both cases, an analog of the Connes–Hochschild–Kostant–Rosenberg theorem describing the structure of Hopf cyclic cohomology in terms of equivariant cohomology and other more geometric cohomology groups is proved.