We prove a comparison result between two duality statements - Takai duality, which is implemented by the crossed product functor - G: KKG → KKG on equivariant Kasparov categories; and Treumann duality, which asserts the existence of an exotic equivalence of stable ∞-categories Mod(KUₚ[G])ᶠᵗ Mod(KUₚ[ G])ᶠᵗ given by tensoring with a particular (G, G)-bimodule ME and p-completing.
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Vikram Nadig (2024) studied this question.
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