Universität Hamburg, Deutschland
Brun showed that π0 of every genuine commutative G ring spectrum is a G-Tambara functor. We define a Loday construction for G-Tambara functors for any finite group G. This definition builds on the Hill-Hopkins notion of a G-symmetric monoidal category and the work of Mazur, Hill-Mazur and Hoyer who prove that for any finite group and any G-Tambara functor R there is a compatible definition of tensoring a finite G-set X with R. We extend this to a tensor product of a G-Tambara functor with a finite simplicial G-set, defining the Loday construction this way. We investigate some of its properties and describe it in examples. This is joint work with Ayelet Lindenstrauss and Foling Zou.