We construct multiplicative twisted versions of differential cohomology theories for all highly structured ring spectra and twists. We prove existence and give a full classification of differential refinements of twists under mild assumptions. Various concrete examples are discussed and related to earlier approaches.
"Twisted differential cohomology." Algebr. Geom. Topol. 19 (4) 1631 - 1710, 2019. https://doi.org/10.2140/agt.2019.19.1631