Structured Real Orientations

In joint work with Ryan Quinn we developed a technique to produce structured equivariant orientations by lifting their underlying structured non-equivariant orientations. This allows us to lift many maps of interest, such as the Hirzebruch level-n genera or the Hahn-Shi orientations. In fact, our result is robust enough to lift structured equivalences resulting in a structured Real Snaith theorem, a structured Real Bökstedt periodicity, and finally the first multiplicative version of the Real Brown-Peterson spectrum.