In this paper we compute the K-theory (algebraic and topological) and
entire periodic cyclic homology for compact quantum groups, define Chern
characters between them and show that the Chern characters in both topological
and algebraic cases are isomorphisms modulo torsion.
The case of compact Lie group C*-algebras was treated in
Non-Commutative Chern characters of compact Lie groups C*-algebras, 0257
,
a revised version of which was accepted for publication in K-Theory.