The Picard group of equivariant stable homotopy theory

Abstract

Let G be a compact Lie group. We describe the Picard group Pic(HoGL) of invertible objects in the stable homotopy category of G-spectra in terms of a suitable class of homotopy representations of G. Combining this with results of tom Dieck and Petrie, which we reprove, we deduce an exact sequence that gives an essentially algebraic description of Pic(HoGL) in terms of the Picard group of the Burnside ring of G. The deduction is based on an embedding of the Picard group of the endomorphism ring of the unit object of any stable homotopy category C in the Picard group of C. © 2001 Academic Press.