  Crystalline graded rings are generalizations of certain classes of rings like
generalized twisted group rings, generalized Weyl algebras, and generalized
skew crossed products. When the base ring is a commutative Dedekind domain, two
constructions are given for producing maximal graded orders. On the way, a new
concept appears, so-called, spectrally twisted group. Some general properties
of it are studied. At the end of the paper several examples are considered.
