I will introduce the notion of jet-equivalence for subsolutions of a fully nonlinear partial differential equation on a manifold. These transformations are quite general and enable one to apply the methods of viscosity theory to establish basic comparison results. One outcome is the ability to solve the Dirichlet problem for G-universal equations on any manifold with a topological G-structure. Another is a basic restriction theorem for general (upper semi-continuous) subsolutions, which has interesting applications to almost complex manifolds.