  Fibered Burnside rings appear as Grothendieck rings of fibered permutation
representations of a finite group, generalizing Burnside rings and monomial
representation rings. Their species, primitive idempotents and their conductors
are of particular interest in representation theory as they encode information
related to the structure of the group. In this note, we introduce fiber change
maps between fibered Burnside rings, and we present results on their
functoriality and naturality with respect to biset operations. We present some
advances on the conductors for cyclic fiber groups, and fully determine them in
particular cases, covering a wide range of interesting examples.
