  We give details of the proof of the remark made in \cite{G2} that the Chern
characters of the canonical generators on the K homology of the quantum group
$SU_q(2)$ are not invariant under the natural $SU_q(2)$ coaction. Furthermore,
the conjecture made in \cite{G2} about the nontriviality of the twisted Chern
character coming from an odd equivariant spectral triple on $SU_q(2)$ is
settled in the affirmative.
