We report on new techniques to study equivariant multiplicative structures. Our main application is an Eρ-structure on BPR, as well as Eρ-refinements of the Hahn–Shi Real orientations, and of the Hirzebruch level-n genus. The formal ingredient is a good theory of
modules allowing us to equivariantize Antolín-Camarena–Barthel’s universal property of multiplicative Thom spectra. This is joint work with Ryan Quinn.