Grothendieck groups of triangulated categories with n-cluster tilting subcategories

Let C be a suitable triangulated category with a Serre functor and an n-cluster tilting subcategory T= add(t), for some integer n>1. In this setup, every indecomposable in T appears in a so called Auslander-Reiten (n+2)-angle in T. We show that the Grothendieck group of C can be expressed as a quotient of the split Grothendieck group of T by some elements determined by the Auslander-Reiten (n+2)-angles in T. We also apply this result to an example.