Real monomial Burnside rings and a decomposition of the the tom Dieck map

Abstract

This thesis is mainly concerned with a decomposition of the reduced tom Dieck map die : f A(RG) → B(G) × into two maps die+ and die− of the real monomial Burnside ring. The key idea is to introduce a real Lefschetz invariant as an element of the real monomial Burnside ring and to generalize the assertion that the image of an RG-module under the tom Dieck map coincides with the Lefschetz invariant of the sphere of the same module.