On graded central simple algebras

This note begins by observing that a graded central simple algebra, graded by an abelian group, is a graded Azumaya algebra and it is free over its centre. For a graded Azumaya algebra A free over its centre R, we show that K1gr(A) is "very close" to K1gr(R), where K1gr(R) is defined to be K1(Pgr(R)). Here Pgr(R) is the category of graded finitely generated projective R-modules and K1, i≥0, are the Quillen K-groups.