  Characterizing sets of permutations whose associated quasisymmetric function
is symmetric and Schur-positive is a long-standing problem in algebraic
combinatorics. In this paper we present a general method to construct
Schur-positive sets and multisets, based on geometric grid classes and the
product operation. Our approach produces many new instances of Schur-positive
sets, and provides a broad framework that explains the existence of known such
sets that until now were sporadic cases.
