We give a result of Auslander-Ringel-Tachikawa type for Gorenstein-projective
modules over a complete Gorenstein order. In particular, we prove that a
complete Gorenstein order is of finite Cohen-Macaulay representation type if
and only if every indecomposable pure-injective object in the stable category
of Gorenstein-projective modules is compact.Comment: Appendix by Rosanna Laking. 22 page