  We construct several pairings in Hopf-cyclic cohomology of (co)module
(co)algebras with arbitrary coefficients. The key ideas instrumental in
constructing these pairings are the derived functor interpretation of
Hopf-cyclic and equivariant cyclic (co)homology, and the Yoneda interpretation
of Ext-groups. As a special case of one of these pairings, we recover the
Connes-Moscovici characteristic map in Hopf-cyclic cohomology. We also prove
that this particular pairing, along with few others, would stay the same if we
replace the derived category of (co)cyclic modules with the homotopy category
of (special) towers of $X$-complexes, or the derived category of mixed
complexes.
