  We prove that for every exact discrete group $\Gamma$, there is an
intermediate C*-algebra between the reduced group C*-algebra and the
intersection of the group von Neumann algebra and the uniform Roe algebra which
is realized as the intersection of a decreasing sequence of isomorphs of the
Cuntz algebra $\mathcal{O}_2$. In particular, when $\Gamma$ has the AP
(approximation property), the reduced group C*-algebra is realized in this way.
We also study extensions of the reduced free group C*-algebras and show that
any exact absorbing or unital absorbing extension of it by any stable separable
nuclear C*-algebra is realized in this way.

Operator Algebras;Group Theory