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We prove the uniqueness of twisted K-theory in both the real and complexcases using the computation of the K-theories of Eilenberg-MacLane spaces dueto Anderson and Hodgkin. As an application of our method, we give somevanishing results for actions of Eilenberg-MacLane spaces on K-theory spectra.

Actions of Eilenberg-MacLane spaces on K-theory spectra and uniqueness of twisted K-theory