K-theory of Azumaya algebras over schemes

Let X be a connected, noetherian scheme and A be a sheaf of Azumaya algebras on X, which is a locally free @X -module of rank a. We show that the kernel and cokernel of K i (X) → K i (A) are torsion groups with exponent a m for some m and any i ≥ 0, when X is regular or X is of dimension d with an ample sheaf (in this case m ≤ d + 1). As a consequence, K i (X, Z/m) K i (A, Z/m), for any m relatively prime to a.