  Let $\Gamma$ be a discrete countable group. Consider the crossed product
C$^\ast$-algebra $\mathfrak{R}(\Gamma) = C^{\ast}(\Gamma \rtimes
l^{\infty}(\Gamma))$.
  Let $G$ be a larger discrete group, containing $\Gamma$ as an almost normal
subgroup. Consequently $G$ acts by partial isomorphisms on $G$ and hence on
$\mathfrak {R}(\Gamma)$. Let $\mathfrak{R}_G(\Gamma)$ be the crossed product
$C^{\ast}$ - algebra $C^{\ast}(G \times (\mathfrak{R}(\Gamma))$. The
C$^\ast$-algebra $\mathfrak{R}_G(\Gamma)$ has a natural representation into
$\mathcal B(\ell ^2(\Gamma))$ and hence also admits a representation
$\Pi_{\mathcal{Q}}$ into the Calkin algebra $\mathcal{Q}(\ell ^2(\Gamma))$.
  Let $G\rtimes \Gamma=\Gamma\times \Gamma^{\rm op} $ and assume that $\Gamma$
is exact. Assume that the non-trivial conjugation orbits under the action of
$\Gamma$, having non amenable stabilizers, are separated, in a suitable chosen
profinite topology, from the identity element in $\Gamma$. We also assume
natural amenability conditions on the dynamics of the action of $\Gamma\times
\Gamma^{\rm op}$ on cosets of amenable subgroups. Then $\Pi_{\mathcal Q}$
factorises to a representation of $C^{\ast}_{\rm red}(G \rtimes
\mathfrak{R}(\Gamma))$. In particular the groups ${\mathop{SL}}_3(\mathbb Z)$,
${\mathop{\rm PGL}}_2(\mathbb Z[\frac{1}{p}])$ have the Akemann-Ostrand
property.
  This implies, using the solidity property of Ozawa ([Oz]), that the group von
Neumann algebras, $\mathcal L({\mathop{SL}}_3(\mathbb Z))$ and $\mathcal
L({\mathop{SL}}_n(\mathbb Z))$, $n\geq 4$, are non-isomorphic.
