A non-Wankel rotary engine having an insert in the peripheral wall of the outer body, the insert being made of a material having a greater heat resistance than that of the peripheral wall, having a subchamber defined therein and having an inner surface bordering the cavity, the subchamber communicating with the cavity through at least one opening defined in the inner surface and having a shape forming a reduced cross-section adjacent the opening, a pilot fuel injector having a tip received in the subchamber, an ignition element having a tip received in the subchamber, and a main fuel injector extending through the housing and having a tip communicating with the cavity at a location spaced apart from the insert.