process

Coarse and equivariant co-assembly maps 89is surjective. Thus we can lift 1 2 RKK G 0 .EGI C; C/ Š K 0.C 0 .EG/ Ì G/ to˛ 2 K top1G; c redG.EG/ Š K top1G; c redG .jGj/ :Then ‰ .˛/ 2 KK G 0 .C; P/ is the desired dual-Dirac morphism.The group Ktop G; xB redG.@Z/ that appears in the above argument is a reducedtopological G-equivariant K-theory for @Z and hence differs from K top G; C.@Z/ .The relationship between these two groups is analysed in [6].References[1] H. Abels, Parallelizability of proper actions, global K-slices and maximal compact subgroups,Math. Ann. 212 (1974/75), 1–19.[2] J. Chabert, S. Echterhoff, H. Oyono-Oyono, Going-down functors, the Künneth Formula,and the Baum-Connes conjecture, Geom. Funct. Anal. 14 (2004), 491–528.[3] A. Connes, A., M. Gromov, H. Moscovici, H. Group cohomology with Lipschitz controland higher signatures, Geom. Funct. Anal. 3 (1993), 1–78.[4] A. N. Dranishnikov, Lipschitz cohomology, Novikov’s conjecture, and expanders, Tr. Mat.Inst. Steklova 247 (2004), 59–73. translation: Proc. Steklov Inst. Math. 4 (247) (2004),50–63.[5] H. Emerson, R. Meyer, Dualizing the coarse assembly map, J. Inst. Math. Jussieu 5 (2006),161–186.[6] H. Emerson, R. Meyer, Euler characteristics and Gysin sequences for group actions onboundaries, Math. Ann. 334 (2006), 853–904.[7] H. Emerson, R. Meyer, A descent principle for the Dirac–dual-Dirac method, Topology 46(2007), 185–209.[8] S. C. Ferry, A. Ranicki, J. Rosenberg, Novikov conjectures, index theorems and rigidity.Vol. 1, London Math. Soc. Lecture Notes Ser. 226, Cambridge University Press, Cambridge1995.[9] N. Higson, Bivariant K-theory and the Novikov conjecture, Geom. Funct. Anal. 10 (2000),563–581.[10] G. G. Kasparov, Equivariant KK-theory and the Novikov conjecture, Invent. Math. 91(1988), 147–201.[11] R. Meyer, R. Nest, The Baum–Connes conjecture via localisation of categories, Topology45 (2006), 209–259.