There is a well-known Quillen's localization sequence for (algebraic) K-theory: $\dots\to K_p^Y(X)\to K_p(X)\to K_p(X-Y)\to \dots$, where $Y\to X$ is a closed embedding of schemes. Now suppose that $X$ is regular (and excellent of finite dimension, if needed). Another well-known fact is that (in this case) the relative K-theory group $K_p^Y(X)$ is isomorphic to $K'_p(Y)$ (some authors denote this by $G_p(Y)$; note that $Y$ is not necessarily regular!).
Now, I tensor this long exact sequence by $\mathbb{Q}$. Can I consider the $i$-th graded piece of the $\gamma$-filtration for this long exact sequence? Certainly, $K^{}(X)\otimes \mathbb{Q}$ and $K^*(X-Y)\otimes \mathbb{Q}$ are endowed with $\gamma$-filtration, but I am not quite sure about $K'_p(Y)\otimes \mathbb{Q}$ (one of my problems here is that I am interested in quite a general situation). Also, could I say that the $i$-th level of the $\gamma$-filtration for $K'_p(Y)$ is some (which one??) level of its niveau filtration?
Which references are most appropriate for these matters? I believe that for rational coefficients these things are easier than for integral ones.
