  We show that the classical Baum-Connes assembly map is quantitatively an
isomorphism for a class of lacunary hyperbolic groups, and we explain how to
see that this class contains many examples of groups that contain graph
sequences of large girth inside their Cayley graphs and therefore do not have
property (A). This includes the known counterexamples to the Baum-Connes
conjecture with coefficients, as well as many other monster groups that have
property (T).
