Hopf algebra ${\mathcal{K}}_n$ and universal Chern classes

We construct a variant ${\mathcal{K}}_n$ of the Hopf algebra ${\mathcal{H}}_n$, which acts directly on the noncommutative model for the generic space of leaves rather than on its frame bundle. We prove that the Hopf cyclic cohomology of ${\mathcal{K}}_n$ is isomorphic to that of the pair $($\mathcal{H}$_n, {\mathop{\rm GL}_n})$ and thus consists of the universal Hopf cyclic classes. We then realize these classes in terms of geometric cocycles.