  In this paper, we conduct further studies on geometric and analytic
properties of asymptotic expansion in measure. More precisely, we develop a
machinery of Markov expansion and obtain an associated structure theorem for
asymptotically expanding actions. Based on this, we establish an analytic
characterisation for asymptotic expansion in terms of the Dru\c{t}u-Nowak
projection and the Roe algebra of the associated warped cones. As an
application, we provide new counterexamples to the coarse Baum-Connes
conjecture.
