Abstract.
We prove a version of the L 2-index Theorem of Atiyah, which uses the universal center-valued trace instead of the standard trace. We construct for G-equivariant K-homology an equivariant Chern character, which is an isomorphism and lives over the ring ℤ⊂λG⊂ℚ obtained from the integers by inverting the orders of all finite subgroups of G. We use these two results to show that the Baum-Connes Conjecture implies the modified Trace Conjecture, which says that the image of the standard trace K 0(C * r (G))→ℝ takes values in λG. The original Trace Conjecture predicted that its image lies in the additive subgroup of ℝ generated by the inverses of all the orders of the finite subgroups of G, and has been disproved by Roy [15].
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Oblatum 10-IV-2001 & 18-X-2001¶Published online: 15 April 2002
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Lück, W. The relation between the Baum-Connes Conjecture and the Trace Conjecture. Invent. math. 149, 123–152 (2002). https://doi.org/10.1007/s002220200215
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DOI: https://doi.org/10.1007/s002220200215