Every projective Schur algebra is Brauer equivalent to a radical abelian algebra

We prove that any projective Schur algebra over a field K isequivalent in Br(K) to a radical abelian algebra. This was conjecturedin 1995 by Sonn and the first author of this paper. As a consequence,we obtain a characterization of the projective Schur group bymeans of Galois cohomology. The conjecture was known for algebrasover fields of positive characteristic. In characteristic zerothe conjecture was known for algebras over fields with a Henselianvaluation over a local or global field of characteristic zero.