  An orthogonal involution on a central simple algebra becoming isotropic over
any splitting field of the algebra, becomes isotropic over a finite odd degree
extension of the base field (provided that the characteristic of the base field
is not 2). The proof makes use of a structure theorem for Chow motives with
finite coefficients of projective homogeneous varieties, of incompressibility
of certain generalized Severi-Brauer varieties, and of Steenrod operations.
