The coadjoint orbit method of Kirillov and Kostant suggests that irreducible unitary representations of a Lie group can be constructed as geometric quantization of coadjoint orbits of the group. It encounters difficulties in the case of noncompact reductive Lie groups. Vogan reformulated the orbit method in terms of quantization of equivariant vector bundles on certain algebraic varieties closely related to coadjoint orbits. I will propose a new way to quantize orbits using deformation quantization of symplectic varieties and their Lagrangian subvarieties and examine Vogan's conjecture. This is based on joint work with Conan Leung and ongoing work with Ivan Losev.

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