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We construct a variant of the Hopf algebra , which acts directly on the noncommutative model for the space of leaves of a general foliation rather than on its frame bundle. We prove that the Hopf cyclic cohomology of is isomorphic to that of the pair and thus consists of the universal Hopf cyclic Chern classes. We also realize these classes in terms of geometric cocycles.
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Henri Moscovici, Bahram Rangipour, Hopf algebras and universal Chern classes. J. Noncommut. Geom. 11 (2017), no. 1, pp. 71–109