Homotopy categories of injective modules over derived discrete algebras

We study the homotopy category $K(\text{Inj}A)$ of all injective modules over a finite dimensional algebra $A$ with discrete derived category. We give a classification of the indecomposable objects of $K(\text{Inj}A)$ for any radical square zero self-injective algebra $A$. In particular, every indecomposable object is endofinite.