I will describe work (joint with Alex Bartel) towards classifying the kernel of the map from the Burnside ring 
of a finite group to the Representation ring of a finite group over a field of positive characteristic. 
For all but one family of soluble groups I will give explicit generators of this kernel.
Time permitting I will discuss a more general approach developed by Alex and myself to tackle 
this sort of classification using the theory of Green Functors.