A first fuel charge having low reactivity (low cetane number) is injected into a rotary engine, e.g., a Wankel engine, sufficiently early during the intake stroke that a subsequent higher-reactivity injected fuel charge forms one or more stratified high-reactivity regions within the engine chamber. Compression ignition then begins at the high-reactivity regions and propagates to the lower-reactivity regions. Appropriate choice of the timings, quantities, and other parameters of the injections can allow control of the timing and rate of combustion, such that work output can be maximized, unburned fuel can be minimized, and chamber temperature can be controlled to reduce heat losses and NOx emissions. As a result, rotary engine efficiency can be enhanced while emissions are reduced. Since the invention can be implemented in a lightweight and compact rotary engine, it is well suited for use in hybrid and compact vehicles.