  We prove that any projective Schur algebra over a field $K$ is equivalent in
$Br(K)$ to a radical abelian algebra. This was conjectured in 1995 by Sonn and
the first author of this paper. As a consequence we obtain a characterization
of the projective Schur group by means of Galois cohomology. The conjecture was
known for algebras over fields of positive characteristic. In characteristic
zero the conjecture was known for algebras over fields with an Henselian
valuation over a local or global field of characteristic zero.
