In this paper Connes and Moscovici introduced the Hopf algebra of transverse differential operators in order to compute the index formula for the diffeomorphism invariant geometry. They developed the theory of cyclic cohomology in the context of Hopf algebras (satisfying some extra condition as the existence of modular pair in involution). They treat the absolute case and only mention that the similar results holds in the relative case. In this paper they define the relative Hopf cyclic cohomology in full generality: however they state that
,,While the meaning of the relative Hopf cyclic group $HP(\mathcal{H}_n,SO(n);\delta,1)$ happened to be quite clear in that particular context, it was not so in the case of non-compact isotropy, for instance for the Lorentz group"
How the relative Hopf cyclic cohomology $HP(\mathcal{H}_n,SO(n);\delta,1)$ is defined (without using the general machinery i.e. Anti-Yetter Drinfeld modules etc)?
