Totaro's question for adjoint groups of types A_{1} and A_{2n}.

Let G be a smooth connected linear algebraic group over a field k, and let X be a G-torsor. Totaro asked: if X admits a zero-cycle of degree d \geq 1, then does X have a closed étalé point of degree dividing d? We give an affirmative answer for absolutely simple classical adjoint groups of types A_1 and A_{2n} over fields of characteristic \neq 2. [ABSTRACT FROM AUTHOR]