Abstract

We prove a comparison result between two duality statements — Takai duality, which is implemented by the crossed product functor $-⋊G:K{K}^G\to K{K}^{\hat{G}}$ on equivariant Kasparov categories, and Treumann duality, which asserts the existence of an exotic equivalence of stable $\infty$-categories

given by tensoring with a particular $(G,\hat{G})$-bimodule $M$.

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