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In this paper, we prove interior a priori first- and second-order estimatesfor solutions of fully nonlinear degenerate elliptic inequalities structuredover the vector fields of Carnot groups, under the main assumption that $u$ issemiconvex along the fields. These estimates for supersolutions are new evenfor linear subelliptic inequalities in nondivergence form, whereas in thenonlinear setting they do not require neither convexity nor concavity on thesecond derivatives. We also exhibit an explicit example showing that horizontal$W^{2,q}$ regularity of Calder\'on-Zygmund type for fully nonlinear subellipticequations posed on the Heisenberg group cannot be in general achieved in therange $q<Q$, $Q$ being the homogeneous dimension of the group.

Interior a priori estimates for supersolutions of fully nonlinear subelliptic equations under geometric conditions