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We develop differential algebraic K-theory for rings of integers in numberfields and we construct a cycle map from geometrized bundles of modules oversuch a ring to the differential algebraic K-theory. We also treat some of thefoundational aspects of differential cohomology, including differentialfunction spectra and the differential Becker-Gottlieb transfer. We then state atransfer index conjecture about the equality of the Becker-Gottlieb transferand the analytic transfer defined by Lott. In support of this conjecture, wederive some non-trivial consequences which are provable by independent means.

Differential function spectra, the differential Becker-Gottlieb transfer, and applications to differential algebraic K-theory