We show that every algebraic group of type over any field becomes split over some field extension of degree dividing . This improves a bound by Tits and, in fact, is optimal.
"Splitting fields for -torsors." Duke Math. J. 121 (3) 425 - 455, 15 February 2004. https://doi.org/10.1215/S0012-7094-04-12132-3