  We introduce an insertion algorithm on Kohnert's combinatorial model for
Demazure characters, generalizing Robinson--Schensted--Knuth insertion on
tableaux. Our new insertion yields an explicit, nonnegative formula expressing
the product of a Demazure character and a Schur polynomial as a sum of Schubert
characters, partially resolving Polo's conjecture that the tensor product of
Demazure modules admits a Schubert filtration.
