  Let $X$ be a connected, noetherian scheme and $\mathcal{A}$ be a sheaf of
Azumaya algebras on $X$ which is a locally free $\mathcal{O}_{X}$-module of
rank $a$. We show that the kernel and cokernel of $K_{i}(X) \to
K_{i}(\mathcal{A}) $ are torsion groups with exponent $a^{m}$ for some $m$ and
any $i\geq 0$, when $X$ is regular or $X$ is of dimension $d$ with an ample
sheaf (in this case $m\leq d+1$). As a consequence, $K_{i}(X,\mathbb Z/m)\cong
K_{i}(\mA,\mathbb Z/m)$, for any $m$ relatively prime to $a$.
