  We study permanence results for almost quasi-isometries, the maps arising
from the Gromov construction of finitely generated random groups that contain
expanders (and hence that are not C*-exact). We show that the image of a
sequence of finite graphs of large girth and controlled vertex degrees under an
almost quasi-isometry does not have Guoliang Yu's property A. We use this
result to broaden the application of Gromov's techniques to sequences of graphs
which are not necessarily expanders. Thus, we obtain more examples of finitely
generated non-C*-exact groups.
