Moduli of Open Stable Maps to a Homogeneous Space

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For L X a Lagrangian embedding associated with a real homogeneous space, we construct the moduli space of stable holomorphic discs mapping to (X,L) as an orbifold with corners equipped with a group action. Some essential constructions involving orbifolds with corners are also discussed, including the existence of fibered products and pushforward and pullback of differential forms with values in a local system.