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