I will describe the classical result of how to recover the homotopy theory of a G-space from the homotopy theory of its system of fixed points, and then I will describe the analogous recent result of Guillou and May for genuine equivariant G-spectra, I will then show how to use this result to construct a new equivariant infinite loop space machine, whose input data is in terms of fixed points. This is joint work with Anna Marie Bohmann.