The functor of p-permutation modules for abelian groups

Let k be a field of characteristic p, where p is a prime number, let ppk(G) be the Grothendieck group of p-permutation kG-modules, where G is a finite group, and let Cppk(G)=C⊗Zppk(G). In this article, we find all the composition factors of the biset functor Cppk restricted to the category of abelian groups.