  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 K_i^{\gr}
(A) is "very close" to K_i^{\gr}(R), where K_i^{\gr} (R) is defined to be
K_i(\Pgr (R)). Here \Pgr (R) is the category of graded finitely generated
projective R-modules and K_i, \,i\geq 0, are the Quillen K-groups.
