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Consider a compact connected orientable CR manifold X 
with the action of a connected compact Lie group G.
Under natural pseudoconvexity assumptions we show
that the CR Guillemin-Sternberg map is Fredholm.
As application we study this map for holomorphic 
line bundles which are positive near the inverse image of zero
by the moment map.
We also show that ``quantization commutes with reduction''
for Sasakian manifolds.