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A celebrated result of Freed, Hopkins and Teleman relates the twisted equivariant K-groups of a compact Lie group G to the Verlinde algebras of G, making these K-groups highly interesting objects to study. In this talk, we explain how a twisted version of the Atiyah--Segal completion theorem connects the twisted equivariant K-theory of G to the Gruher--Salvatore string topology of BG, and discuss a conjecture linking these K-groups to another variant of string topology of BG defined by Chataur and Menichi.