  Namely, we prove that if $G$ is a countable, discrete group and $f\in
M_{n}(\Z(G))$ is invertible on $\ell^{2}(G)^{\oplus n},$ but $f$ is not
invertible in $M_{n}(\Z(G))$, then the measure-preserving action of $G$ on
$X_{f}$ equipped with the Haar measure is weakly equivalent to a Bernoulli
action. We shall in fact prove this weak equivalence in the case that $f$ has a
"formal inverse in $\ell^{2}$".
