  Billey and Braden defined maps on flag manifolds that are the geometric
counterpart of permutation patterns. A section of their pattern map is an
embedding of the flag manifold of a Levi subgroup into the full flag manifold.
We give two expressions for the induced map on cohomology. One is in terms of
generators and the other is in terms of the Schubert basis. We show that the
coefficients in the second expression are naturally Schubert structure
constants and therefore positive. These formulas also hold for K-theory, and
generalize known formulas in type A for cohomology and K-theory.
