  The `transcendental methods' in the algebraic theory of quadratic forms are
based on two major results, proved in the 60's by Cassels and Pfister, and
known as the representation and the subform theorems. A generalization of the
representation theorem was proven by Jean-Pierre Tignol in 1996, in the setting
of central simple algebras with involution. This paper studies the subform
question for orthogonal involutions. A generic characterization of direct
summands is given; an analogue of the subform theorem is proven for division
algebras and algebras of index at most 2.
