Equivariant higher Dixmier-Douady theory for circle actions on UHF-algebras

We develop an equivariant Dixmier-Douady theory for locally trivial bundles of C⁎-algebras with fibre D⊗K equipped a fibrewise T-action, where T denotes the circle group and D=End(V)⊗∞ T-representation V. In particular, we show that T-equivariant ⁎-automorphisms AutT(D⊗K) is infinite loop space giving rise to cohomology ED,T⁎(X). Isomorphism classes then form respect tensor product isomorphic ED,T1(X)≅[X,BAutT(D⊗K)]. compute this tori compare case D=C Brauer actions on base space.