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In this note we give a BRST interpretation of inner product of groupaveraging on de Sitter group SO(2,1). Quantization approaches can be divided intwo classes, without introducing additional degrees of freedom and withintroducing ghosts, antighosts, Lagrange multipliers and canonically conjugatedmomenta. The first class of quantization methods includes Dirac method andgroup averaging method. The Dirac method is based on imposing the constraintconditions on physical states, while in group averaging method one modifies thephysical inner product due to constrains. One should distinguish the abeliancase for which you can have continuous spectrum and discrete spectrum for whichthere are internal topological problems in BRST-BFV approach, and thenon-abelian case.

Group averaging and BRST quantization in de Sitter space