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Abstract. We construct a model of differential K-theory, using the geomet-rically defined Chern forms, whose cocycles are certain equivalence classes of maps into the Grassmannians and unitary groups. In particular, we produce the circle-integration maps for these models using classical homotopy-theoretic constructions, by incorporating certain differential forms which reconcile the incompatibility between these even and odd Chern forms. By the unique-ness theorem of Bunke and Schick, this model agrees with the spectrum-based models in the literature whose abstract Chern cocycles are compatible wit