Differential K-theory as equivalence classes of maps to Grassmannians and unitary groups\

We construct a model of differential K-theory 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 by using certain differential forms that witness the incompatibility between the even and odd universal Chern forms. By the uniqueness theorem of Bunke and Schick, this model agrees with the spectrum based models in the literature whose nongeometrically defined Chern cocycles are compatible with the delooping maps of the spectrum. These constructions favor geometry over homotopy theory.