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We construct string topology operations in twisted  K ‐theory. We study the examples given by symplectic Grassmannians, computing  K  *   τ  ( L ℍ P  ℓ ) in detail. Via the work of Freed–Hopkins–Teleman, these computations are related to completions of the Verlinde algebras of Sp( n ). We compute these completions, and other relevant information about the Verlinde algebras. We also identify the completions with the twisted  K ‐theory of the Gruher–Salvatore pro‐spectra. Further comments on the field‐theoretic nature of these constructions are made.

The symplectic Verlinde algebras and string K ‐theory