  We use the Witten index in the open string sector to determine tadpole
charges of orientifold planes and D-branes. As specific examples we consider
type I compactifications on Calabi Yau manifolds and noncompact orbifolds. The
tadpole constraints suggest that the standard embedding is not a natural choice
for the gauge bundle. Rather there should be a close connection of the gauge
bundle and the spin bundle. In the case of a four fold, the standard embedding
does not in general fulfill the tadpole conditions. We show that this agrees
with the Green-Schwarz mechanism. In the case of noncompact orbifolds we are
able to solve the tadpole constraints with a gauge bundle, which is related to
the spin bundle. We compare these results to anomaly cancellation on the fixed
plane of the orbifold. In the case of branes wrapping noncompact cycles, there
are fractional intersection numbers and anomaly coefficients, which we explain
in geometric terms.
