Barker, L.Tuvay, İ.2016-02-082016-02-0820120021-8693http://hdl.handle.net/11693/21567We introduce a restriction morphism, called the Boltje morphism, from a given ordinary representation functor to a given monomial Burnside functor. In the case of a sufficiently large fibre group, this is Robert Boltje's splitting of the linearization morphism. By considering a monomial Lefschetz invariant associated with real representation spheres, we show that, in the case of the real representation ring and the fibre group {±1}, the image of a modulo 2 reduction of the Boltje morphism is contained in a group of units associated with the idempotents of the 2-local Burnside ring. We deduce a relation on the dimensions of the subgroup-fixed subspaces of a real representation. © 2011 Elsevier Inc.EnglishMonomial Lefschetz invariantsReal representation spheresReal representations of finite groupsprimary 20C15secondary 19A22Article10.1016/j.jalgebra.2011.12.009218693