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Algebraic $K$-theory of Fredholm modules and KK-theory

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Tamaz Kandelaki

Kasparov $KK$-groups $KK(A,B)$ are represented as homotopy groupsof the
Pedersen-Weibel nonconnective algebraic $K$-theory spectrumof the additive
category of Fredholm $(A,B)$-bimodules for $A$ and$B$, respectively,
a separable and $\sigma$-unital triviallygraded real or complex $C^*$-algebra
acted upon by a fixed compactmetrizable group.

Journal of Homotopy and Related Structures, Vol. 1(2006), No. 1, pp. 195-218
http://jhrs.rmi.acnet.ge/volumes/2006/n1a9/