An internal combustion engine includes a cylinder that is connectable to an intake manifold through an intake valve, to an exhaust manifold through an exhaust valve, and to a transfer manifold through transfer and combustion valves. A fuel injector associated with the cylinder is adapted to provide fuel to the cylinder. During operation, the cylinder performs an intake stroke, followed by a compression stroke. A compressed charge from the cylinder passes to and is collected in the transfer manifold through the transfer valve. The cylinder is filled by a compressed charge from the transfer manifold through the combustion valve at the same time as the fuel injector provides fuel. The cylinder then undergoes combustion and exhaust strokes. In this way, cylinder operation alternates between combustor and compressor split combustion modes.