Abstract: In classical equivariant homotopy theory, fixed point functors play a crucial role in identifying genuine G-spectra. However, in motivic homotopy theory, this identification is not as straightforward. This discrepancy arises from the fact that the category of motivic G-spectra is not solely generated by objects resembling G-orbits.
In this talk, we will introduce the concept of gerbes and explore how gerbe fixed point functors form a conservative family. We will delve into the reasons behind this conservativity and its implications. If time permits, we will also provide a brief overview of how this conservative family, in conjunction with other theorems, leads to the development of motivic spectral Mackey functors. 