Ring of subquotients of a finite group I: Linearization

We introduce the ring Λ(G) of subquotients of a finite group G. As an abelian group, it is free on the set of conjugacy classes of subquotients of the group G. The ring Λ(G) integrally extends the Burnside ring and there is a linearization map with range the Grothendieck ring of the Mackey algebra.