Derived discrete Hopf algebras with the Chevalley property

We try to classify Hopf algebras with the Chevalley property according to their derived representation type. We show that a finite-dimensional indecomposable non-semisimple Hopf algebra $H$ with the Chevalley property is derived discrete if and only if it is isomorphic to $(A(n,2,\mu ,-1){)}^{\ast }$. Besides, we give a description for the indecomposable objects in ${\mathcal{D}}^b((A(n,2,\mu ,-1){)}^{\ast })$ and determine their tensor products.