### Cohen-Macaulay modules over two-dimensional graph orders

For a split graph order ℒ over a complete local regular domain $\mathcal{O}$ of dimension 2 the indecomposable Cohen-Macaulay modules decompose - up to irreducible projectives - into a union of the indecomposable Cohen-Macaulay modules over graph orders of type •—• . There, the Cohen-Macaulay modules filtered by irreducible Cohen-Macaulay modules are in bijection to the homomorphisms $\varphi :\mathcal{O}{L}^{\left(\mu \right)}\to \mathcal{O}{L}^{\left(\nu \right)}$ under the bi-action of the groups $\left(Gl\right(\mu ,\mathcal{O}L),Gl(\nu ,\mathcal{O}L\left)\right)$, where $\mathcal{O}L=\mathcal{O}/\u3008\pi \u3009$ for a prime π. This problem strongly depends on the nature of $\mathcal{O}L$. If $\mathcal{O}L$ is regular,...