A split-cycle air hybrid engine operatively connecting an air reservoir to a split cycle engine is provided. A power piston is received within a power cylinder and operatively connected to a crankshaft such that the power piston reciprocates through an expansion stroke and an exhaust stroke during a single revolution of the crankshaft. A compression piston is received within a compression cylinder and operatively connected to the crankshaft such that the compression piston reciprocates through an intake stroke and a compression stroke in a single rotation of the crankshaft. The compression cylinder is selectively controllable to place the compression piston in a compression mode or an idle mode. An air reservoir is operatively connected between the compression cylinder and the power cylinder and selectively operable to receive compressed air from the compression cylinder and to deliver compressed air to the power cylinder for use in transmitting power to the crankshaft during engine operation.