Let A be a ring with 1, C the center of A and G′ an
inner automorphism group of A induced by {Uα in A/α in a finite
group G whose order is invertible}. Let AG′ be the fixed subring of
A under the action of G′.If A is a Galcis extension of AG′ with
Galois group G′ and C is the center of the subring ∑αAG′Uα then
A=∑αAG′Uα and the center of AG′ is also C. Moreover, if
∑αAG′Uα is Azumaya over C, then A is a projective group ring.