Tori in Quasi-Split Groups

Let G be a connected quasi-split semisimple algebraic group over a field k. Let S be a maximal k-split torus and T=Z(S) its centraliser. Then T is a maximal k-torus in G. The normaliser N(S)of S is also the normaliser N(T) of T . All these groups are defined over k and hence also N(T)/Z(T)=W, a finite group. Suppose now that T'⊂G is any maximal k-torus. Then there is an element g∈G(k_s)/ such that gTg-¹=T' where k_s is a separable closure of k. If G is the Galois group of k_s over k and σ∈G, evidently σ(g)Tσ(g)^-1=σ(gTg^-1)=T'.