  A famous theorem of D. Orlov describes the derived bounded category of
coherent sheaves on projective hypersurfaces in terms of an algebraic
construction called graded matrix factorizations. In this article, I implement
a proposal of E. Segal to prove Orlov's theorem in the Calabi-Yau setting using
a globalization of the category of graded matrix factorizations (graded
D-branes). Let X be a projective hypersurface. Already, Segal has established
an equivalence between Orlov's category of graded matrix factorizations and the
category of graded D-branes on the canonical bundle K of the ambient projective
space. To complete the picture, I give an equivalence between the homotopy
category of graded D-branes on K and Dcoh(X). This can be achieved directly and
by deforming K to the normal bundle of X, embedded in K and invoking a global
version of Kn\"{o}rrer periodicity. We also discuss an equivalence between
graded D-branes on a general smooth quasi-projective variety and on the formal
neighborhood of the singular locus of the zero fiber of the potential.
