A split-cycle air hybrid engine with improved efficiency is disclosed in which the centerline of a compression cylinder is positioned at a non-zero angle with respect to the centerline of an expansion cylinder such that the engine has a V-shaped configuration. In one embodiment, the centerlines of the respective cylinders intersect an axis parallel to, but offset from, the axis of rotation of the crankshaft. Modular crossover passages, crossover passage manifolds, and associated air reservoir valve assemblies and thermal regulation systems are also disclosed.