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"We develop differential algebraic K-theory for rings of integers in number fields and we construct a cycle map from geometrized bundles of modules over such a ring to the differential algebraic K-theory. We also treat some of the foundational aspects of differential cohomology, including differential function spectra and the differential Becker-Gottlieb transfer. We then state a transfer index conjecture about the equality of the Becker-Gottlieb transfer and the analytic transfer defined by Lott. In support of this conjecture, we derive some non-trivial consequences which are provable by independent means"--

K-theory. --- Differential topology. --- $K$-theory -- Topological $K$-theory -- Twisted $K$-theory; differential $K$-theory. --- Manifolds and cell complexes -- Differential topology -- Algebraic topology on manifolds.