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

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