The unbounded Kasparov product by a differentiable module

In this paper we investigate the unbounded Kasparov product between a differentiable module and an cycle of very general kind that includes all modules hence also spectral triples. Our assumptions on are weak do in particular not require it satisfies any smooth projectivity conditions. The algebras work with furthermore required to possess approximate identity. lack adequate condition our entails usual class is flexible enough accommodate becomes necessary twist commutator by automorphism.