  For an algebra B with an action of a Hopf algebra H we establish the pairing
between even equivariant cyclic cohomology and equivariant K-theory for B. We
then extend this formalism to compact quantum group actions and show that
equivariant cyclic cohomology is a target space for the equivariant Chern
character of equivariant summable Fredholm modules. We prove an analogue of
Julg's theorem relating equivariant K-theory to ordinary K-theory of the
C*-algebra crossed product, and characterize equivariant vector bundles on
quantum homogeneous spaces.
