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The theory of biset functors developed by Serge Bouc has been instrumental inthe study of the unit group of the Burnside ring of a finite group, inparticular for the case of p-groups. The ghost ring of the Burnside ringdefines an inflation functor, and becomes a useful tool in studying theBurnside ring functor itself. We are interested in studying the unit group ofanother representation ring: the trivial source ring of a finite group. In thisarticle, we show how the unit groups of the trivial source ring and itsassociated ghost ring define inflation functors. Since the trivial source ringis often seen as connecting the Burnside ring to the character ring and Brauercharacter ring of a finite group, we study all these representation rings atthe same time. We point out that restricting all of these representation rings'unit groups to their torsion subgroups also give inflation functors, which wecan completely determine in the case of the character ring and Brauer characterring.

Unit Groups of Representation Rings and their Ghost Rings as Inflation Functors