Abstract
We 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 Boltjeʼs 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.
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