On when a graded ring is graded equivalent to a crossed product

Let R be a ring graded by a group G. We are concerned with describing those G-graded rings that are graded equivalent to G-crossed products. We give necessary and sufficient conditions for when a strongly graded ring is graded equivalent to a crossed product, provided that the 1-component is either Azumaya or semiperfect. Our result uses the torsion product theorem of Bass and Guralnick. We also construct various examples of such rings.