Due to the Quillen-Lichtenbaum conjecture (now proven by Rost, Voevodsky, and Weibel), the map $K_\ast(X,\mathbb{Z}/n)\rightarrow K_\ast^{et}(X,\mathbb{Z}/n)$ from algebraic K-theory to etale K-theory is an isomorphism when $\ast$ is at least the mod $n$ etale cohomological dimension of $X$. (I think $X$ is a smooth scheme of finite type over a field which contains $1/n$.) In fact, we know from Thomason that $K_\ast^{et}$ can be obtained from $K_\ast$ by inverting a Bott element.
How can we measure the difference between $K_\ast$ and $K_\ast^{et}$? Since it is all concentrated within the etale cohomological dimension of $X$, I would guess the difference would look something like etale cohomology. Is there a long exact sequence?
