Smooth Connes--Thom isomorphism, cyclic homology, and equivariant quantisation

Using a smooth version of the Connes–Thom isomorphism in Grensing’s bivariant K-theory for locally convex algebras, we prove an equivariant version of the Connes–Thom isomorphism in periodic cyclic homology. As an application, we prove that periodic cyclic homology is invariant with respect to equivariant strict deformation quantization.