Let $Q$ be a Dynkin quiver. Let $\mathbb CQ$ be its complex path algebra. It is defined in a way such that modules over $\mathbb CQ$ are the same as representations of the quiver $Q$. Let's write $\mathrm{mod}(\mathbb CQ)$ for the finite-dimensional $\mathbb CQ$-modules. There is a beautiful description of the bounded derived category $D^b(\mathrm{mod}(\mathbb CQ))$ in terms of translation quivers and mesh relations, see Happel: On the derived category of a finite-dimensional algebra.

I would be interested in a similar description of the bounded derived category $D^b(\mathrm{mod}(\mathbb ZQ))$ of finitely generated modules over the path *ring* $\mathbb ZQ$. More precisely, I am looking for a result along the lines "There is a nicely characterized full subcategory in $D^b(\mathrm{mod}(\mathbb ZQ))$ which, after tensoring with $\mathbb C$, becomes equivalent to $D^b(\mathrm{mod}(\mathbb CQ))$." Since Happel's paper is from 1987, I believe someone must have tried to generalise his results to integer representations since then.