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We discuss a new strategy for the computation of the Hopf-cyclic cohomology of the Connes–Moscovici Hopf algebra $$\mathcal{H}_n$$ Hn . More precisely, we introduce a multiplicative structure on the Hopf-cyclic complex of $$\mathcal{H}_n$$ Hn , and we show that the van Est type characteristic homomorphism from the Hopf-cyclic complex of $$\mathcal{H}_n$$ Hn to the Gelfand–Fuks cohomology of the Lie...
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