Auslander-Reiten theory of wild algebras known in examples?

For self-injective Koszul algebras of Loewy length greater than three such that the Yoneda algebra is Noetherian, all (stable) components of the Auslander-Reiten quiver for graded modules are of the form $\mathbb Z A_{\infty}$ (Martinez-Villa, Zacharia: Approximation with modules having linear resolution).

It shouldn't be too hard to find examples where all modules are gradeable, it is more difficult to keep track of graded shifts within each component. The easy way out is to say that each (ungraded) component is of the form $\mathbb Z A_{\infty}/G$ for some group of automorphisms $G$. (Edit: Also known as a tube when $G$ is non-trivial.)