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Let $M$ be a strongly pseudoconvex complex $G$-manifold with compact quotient$M/G$. We provide a simple condition on forms $\alpha$ sufficient for theregular solvability of the equation $\square u=\alpha$ and other problemsrelated to the $\bar\partial$-Neumann problem on $M$.

A transversal Fredholm property for the $\bar\partial$-Neumann problem on $G$-bundles