On Auslander–Reiten components and trivial source lattices for integral group rings

Let G be a finite group, O a complete discrete valuation ring of characteristic zero with residue class field O/πO of prime characteristic and B a block of the group ring OG. Suppose that B is of infinite representation type and O is large enough. Let Γ(B) be the Auslander–Reiten quiver of B and Θ a connected component of Γ(B). In this paper, we show that if Θ contains a trivial source OG-lattice T then the tree class of the stable part of Θ is A∞ and T lies at the end of Θ.