Ring of subquotients of a finite group II: Pure bisets

This sequel to O. Coşkun (2009) [6] focuses on the structure of the ring Λ(G) of subquotients of the finite group G. We show that this ring is isomorphic with the Grothendieck ring of the category of pure (G,G)-bisets, which are bisets containing no isogations. We also determine, over a field of characteristic zero, the Mackey functor structure and the primitive idempotents of Λ(G). Main tool of this determination is the marks of subquotients on each other.