ag.algebraic geometry – $K$-theory of formal completion

Let $X_Z$ be the formal completion of $X$ along $Z$. An application of devissage implies that the pushforward map from the reduced scheme to the scheme induces isomorphisms on $G$-theory groups, so $G_i(Z)cong G_i(X_Z)$. If $X$ and $Z$ are smooth is it true that $K_i(Z)cong K_i(X_Z)$? If so does the pullback induce the other isomorphism from $K_i(X_Z)$ to $K_i(Z)$?