Geodesic
Classifying spaces for equivariant $K$-theory
Sbornik. Mathematics, Tome 24 (1974) no. 1, pp. 31-48

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In this paper the methods of M. Karoubi (RZh.Mat., 1971, 2A466) are generalized to the case of equivariant $K$-theory. The sets of Fredholm operators in certain (Hilbert) spaces of representations of finite groups $G$ are described which are classifying spaces for equivariant $K$-functors. The results were announced in the paper RZh.Mat., 1972, 10A375. Bibliography: 16 titles. 
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P. A. Kuchment; A. A. Pankov. Classifying spaces for equivariant $K$-theory. Sbornik. Mathematics, Tome 24 (1974) no. 1, pp. 31-48. http://geodesic.mathdoc.fr/item/SM_1974_24_1_a2/