Algebraic \(K\)-theory of Fredholm modules and \(KK\)-theory (Q2381414)

For \(A\) a separable \(C^{*}\)-algebra and \(B\) a \(\sigma\)-unital \(C^{*}\)-algebra, let \({\mathcal R}ep(A,B)\) be the \(C^{*}\)-category of Fredholm \((A,B)\)-bimodules. The author shows that \(\pi_{n}\) of the Pedersen-Weibel connective algebraic \(K\)-theory spectrum of \({\mathcal R}ep(A,B)\) is isomorphic to the Kasparov group \(KK_{n-1}(A,B)\).