Let $S$ be a scheme and let $G\to S$ be a reductive group scheme. Then $G$ admits a maximal torus etale-locally, and any two maximal tori are conjugate etale-locally, by Theorem 3.2.6 and Corollary 3.2.7 in [B. Conrad, Reductive group schemes] http://math.stanford.edu/~conrad/papers/luminysga3.pdf.
As pointed out in the book, below Proposition 3.1.9 and at the beginning of Chapter 4, the existence of maximal tori can be achieved Zariski-locally (cf. [SGA3, XIV, 3.20]). My question is the following
Let $T$ and $T'$ be maximal tori in $G$ defined over $S$, are they conjugate Zariski-locally?
In my case, $T$ is split over $S$, and $S$ is affine with $Pic(S)=0$.
I would appreciate any remarks!