Hopf-cyclic cohomology of the Connes-Moscovici Hopf algebras with infinite dimensional coefficients

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We discuss a new strategy for the computation of the Hopf-cyclic cohomology of the Connes-Moscovici Hopf algebra Hₙ. More precisely, we introduce a multiplicative structure on the Hopf-cyclic complex of Hₙ, and we show that the van Est type characteristic homomorphism from the Hopf-cyclic complex of Hₙ to the Gelfand-Fuks cohomology of the Lie algebra Wₙ of formal vector fields on Rⁿ respects this multiplicative structure. We then illustrate the machinery for n=1.