  By a result of Nagy, the C*-algebra of continuous functions on the
q-deformation G_q of a simply connected semisimple compact Lie group G is
KK-equivalent to C(G). We show that under this equivalence the K-homology class
of the Dirac operator on G_q, which we constructed in an earlier paper,
corresponds to that of the classical Dirac operator. Along the way we prove
that for an appropriate choice of isomorphisms between completions of U_q(g)
and U(g) a family of Drinfeld twists relating the deformed and classical
coproducts can be chosen to be continuous in q.
