For a given saturated fusion system F we define the ring A(S)^F of the F-invariants of the Burnside ring functor. We show how this ring is related to the Burnside ring of the fusion system F and how it appears naturally in the analogue of Segal's conjecture for the classifying spectrum ¿F. We give an explicit description of A(S)^F and we prove it is a local ring.
- fusion systems
- Burnside ring