  We examine the cokernel of the canonical homomorphism from the trivial source
ring of a finite group to the ring of $p$-rational complex characters. We use
Boltje and Co\c{s}kun's theory of fibered biset functors to determine the
structure of the cokernel. An essential tool in the determination of this
structure is Bouc's theory of rational $p$-biset functors.
