  We show how methods from K-theory of operator algebras can be applied in a
completely algebraic setting to define a bivariant, matrix-stable,
homotopy-invariant, excisive K-theory of algebras over a fixed unital ground
ring H, 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
kk_*(H,A)=KH_*(A).
  We show further that some calculations from operator algebra KK-theory, such
as the exact sequence of Pimsner-Voiculescu, carry over to algebraic kk.
