The Picard group in equivariant homotopy theory via stable module categories

Abstract We develop a mechanism of “isotropy separation for compact objects” that explicitly describes an invertible ‐spectrum through its collection of geometric fixed points and gluing data located in certain variants of the stable module category. As an application, we carry out a complete analysis of possible combinations of geometric fixed points of invertible ‐spectra in the case . A further application is given by showing that the Picard groups of and a category of derived Mackey functors agree.