UC Santa Cruz

Let A be an abelian group and let K be a field of characteristic zero containing roots of unity of all orders equal to finite element orders in A. In this thesis we prove foundational properties of the A-fibered Burnside ring functor B^A_K as an A-fibered biset functor over K. This includes the determination of the lattice of subfunctors of B^A_K and the determination of the composition factors of B^A_K. The results of the paper extend results of Coşkun and the author for the A-fibered Burnside ring functor restricted to p-groups and results of Bouc in the case that A is trivial, i.e., the case of the Burnside ring functor over fields of characteristic zero.