  We consider functors from the category of locally convex algebras to abelian
groups and prove invariance under smooth homotopies for weakly J-stable
algebras, where J is a harmonic operator ideal. This applies in particular to
negative algebraic K-theory. We develop the technology of Kasparov modules in
an algebraic setting in order to obtain the results. The article also includes
a computation of the first algebraic K-theory of harmonic operator ideals.
