Split exactness, operator homotopy and stable uniqueness in KK

We develop important properties of the KK-functor on the basis of split exactness. In particular we discuss two slightly different short proofs for the existence of the Kasparov product and its associativity. We use the approach with quasihomomorphisms to obtain a short proof of the fact that operator homotopy implies homotopy . Using an idea of Gabe-Szabo we also deduce from this the ‘stable uniqueness theorem’ of Dadarlat-Eilers by a very short argument.