How to prove the Baum-Connes conjecture for the groups Sp(n, 1) ?

We present a programme of proof of the Baum-Connes conjecture with coefficients for G=Sp(n,1) or F4(-20), i.e. simple Lie groups of real rank one having Kazhdan's property (T). We use the geometry of the boundary sphere to produce a G-Fredholm module, together with a homotopy to the trivial representation through uniformly bounded representations. The strip of uniformly bounded representations of M. Cowling plays here the role of the complementary series. We explain how, modulo some conjectural estimates, this construction would prove the conjecture. (C) 2019 Elsevier B.V. All rights reserved.