  We study the quantum isometry groups of the noncommutative Riemannian
manifolds associated to discrete group duals. The basic representation theory
problem is to compute the law of the main character of the relevant quantum
group, and our main result here is as follows: for the group Z_s^{*n}, with s>4
and n>1, half of the character follows the compound free Poisson law with
respect to the measure $\underline{\epsilon}$/2, where $\epsilon$ is the
uniform measure on the s-th roots of unity, and
$\epsilon\to\underline{\epsilon}$ is the canonical projection map from complex
to real measures. We discuss as well a number of technical versions of this
result, notably with the construction of a new quantum group, which appears as
a "representation-theoretic limit", at s equal to infinity.
