In this talk we introduce a new Hopf algebra with a characteristic map that captures the twisted local index formula on the groupoid action algebra. In contrast with the Connes-Moscovici Hopf algebra the cohomology of this new

Hopf algebra is comprised of all universal Chern classes. This proves that the cyclic cohomology class of the twisted index cocycle is primary. The talk is based on the collaboration with Henri Moscovici.