The maximal coarse Baum-Connes conjecture for spaces which admit a   fibred coarse embedding into Hilbert space
  We introduce a notion of fibred coarse embedding into Hilbert space for metric spaces, which is a generalization of Gromov's notion of coarse embedding into Hilbert space. It turns out that a large class of expander graphs admit such an embedding. We show that the maximal coarse Baum-Connes conjecture holds for metric spaces with bounded geometry which admit a fibred coarse embedding into Hilbert space. 
Xiaoman Chen, Qin Wang, Guoliang Yu
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