Equivariant geometric K-homology for compact Lie group actions

@article{Baum2010EquivariantGK,
  title={Equivariant geometric K-homology for compact Lie group actions},
  author={Paul Frank Baum and Herv'e Oyono-Oyono and Thomas Schick and Michael Walter},
  journal={Abhandlungen aus dem Mathematischen Seminar der Universit{\"a}t Hamburg},
  year={2010},
  volume={80},
  pages={149-173}
}
Let G be a compact Lie-group, X a compact G-CW-complex. We define equivariant geometric K-homology groups $K^{G}_{*}(X)$, using an obvious equivariant version of the (M,E,f)-picture of Baum-Douglas for K-homology. We define explicit natural transformations to and from equivariant K-homology defined via KK-theory (the “official” equivariant K-homology groups) and show that these are isomorphisms. 
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