Let G be a locally compact group with cocompact connected component. We prove that the assembly map from the topological K-theory of G to the K-theory of the reduced C-algebra of G is an isomorphism. The same is shown for the groups of -rational points of any linear algebraic group over a local field of characteristic zero.
@article{PMIHES_2003__97__239_0, author = {Chabert, J\'er\^ome and Echterhoff, Siegfried and Nest, Ryszard}, title = {The {Connes-Kasparov} conjecture for almost connected groups and for linear $p$-adic groups}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {239--278}, publisher = {Springer}, volume = {97}, year = {2003}, doi = {10.1007/s10240-003-0014-2}, zbl = {1048.46057}, language = {en}, url = {http://archive.numdam.org/articles/10.1007/s10240-003-0014-2/} }
TY - JOUR AU - Chabert, Jérôme AU - Echterhoff, Siegfried AU - Nest, Ryszard TI - The Connes-Kasparov conjecture for almost connected groups and for linear $p$-adic groups JO - Publications Mathématiques de l'IHÉS PY - 2003 SP - 239 EP - 278 VL - 97 PB - Springer UR - http://archive.numdam.org/articles/10.1007/s10240-003-0014-2/ DO - 10.1007/s10240-003-0014-2 LA - en ID - PMIHES_2003__97__239_0 ER -
%0 Journal Article %A Chabert, Jérôme %A Echterhoff, Siegfried %A Nest, Ryszard %T The Connes-Kasparov conjecture for almost connected groups and for linear $p$-adic groups %J Publications Mathématiques de l'IHÉS %D 2003 %P 239-278 %V 97 %I Springer %U http://archive.numdam.org/articles/10.1007/s10240-003-0014-2/ %R 10.1007/s10240-003-0014-2 %G en %F PMIHES_2003__97__239_0
Chabert, Jérôme; Echterhoff, Siegfried; Nest, Ryszard. The Connes-Kasparov conjecture for almost connected groups and for linear $p$-adic groups. Publications Mathématiques de l'IHÉS, Tome 97 (2003), pp. 239-278. doi : 10.1007/s10240-003-0014-2. http://archive.numdam.org/articles/10.1007/s10240-003-0014-2/
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