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We study the homotopy category $ K(\Inj A)$ of all injective modules over afinite dimensional algebra $A$ with discrete derived category. We give aclassification of the indecomposable objects of $ K(\Inj A)$ for any radicalsquare zero self-injective algebra $A$. In particular, every indecomposableobject is endofinite.

Homotopy categories of injective modules over derived discrete algebras