  We prove that, if M is a compact oriented manifold of dimension 4k+3, where
k>0, such that pi_1(M) is not torsion-free, then there are infinitely many
manifolds that are homotopic equivalent to M but not homeomorphic to it. To
show the infinite size of the structure set of M, we construct a secondary
invariant tau_(2): S(M)-->R that coincides with the rho-invariant of
Cheeger-Gromov. In particular, our result shows that the rho-invariant is not a
homotopy invariant for the manifolds in question.
