  The Chern-Dold character of a cohomology theory E is a canonical
transformation $E\rightarrow HV$ to ordinary cohomology. A spectrum
representing E gives homotopy theoretic cocycles for E, while HV can be
represented by singular cocycles. We construct a refinement of the Chern-Dold
character to a transformation of the cocycle categories that takes the
homotopical composition to the addition of singular cocycles. This is applied
to construct additive structures at the level of differential cocycles for
generalized differential cohomology.
