We show how methods from K-theory of operator algebras can be applied in a completely algebraic setting to define a bivariant, M∞-stable, homotopy-invariant, excisive K-theory of algebras over a fixed unital ground ring H, (A, B) ↦ kk*(A, B), which is universal in the sense that it maps uniquely to any other such theory. It turns out kk is related to C. Weibel's homotopy algebraic K-theory, KH. We prove that, if H is commutative and A is central as an H-bimodule, then
We show further that some calculations from operator algebra KK-theory, such as the exact sequence of Pimsner-Voiculescu, carry over to algebraic kk.
© Walter de Gruyter