  We prove new Skoda-type division, or ideal membership, theorems. We work in a
geometric setting of line bundles over Kahler manifolds that are Stein away
from an analytic subvariety. (This includes complex projective manifolds.) Our
approach is to combine the twisted Bochner-Kodaira Identity, used in the
Ohsawa-Takegoshi Theorem, with Skoda's basic estimate for the division problem.
Techniques developed by McNeal and the author are then used to provide many
examples of new division theorems. Among other applications, we give a
modification of a recent result of Siu regarding effective finite generation of
certain section rings.
