A rotary engine comprising: a stator body having an internal cavity defined by two axially spaced apart end walls and a peripheral wall extending between the end walls, the cavity having an epitrochoid shape defining two lobes; a rotor body having three circumferentially spaced apex portions, the rotor body being engaged to an eccentric portion of a shaft to rotate and perform orbital revolutions within the cavity with each of the apex portions remaining in sealing engagement with the peripheral wall and separating three rotating chambers of variable volume defined in the cavity around the rotor body; an insert (34; 134; 234) in the peripheral wall of the stator body, the insert (34; 134; 234) having an inner surface (66; 166; 266) bordering the cavity; an ignition element having a tip received in the subchamber; and a main fuel injector extending through the peripheral wall and having a tip communicating with the cavity at a location spaced apart from the insert (34; 134; 234); characterised in that the insert (34; 134; 234) is made of a material having a greater heat resistance than that of the peripheral wall, and has a subchamber defined therein, the subchamber communicating with the cavity through at least one opening defined in the inner surface (66; 166; 266) and having a shape forming a reduced cross-section adjacent the opening; the ignition element is received in an ignition element hole defined in the insert (34; 134; 234); by further comprising a pilot fuel injector having a tip received in the subchamber; and in that the volume of each chamber varies between a minimum volume and a maximum volume with a difference between the maximum volume and the minimum volume defining a displacement volume, the subchamber having a volume of at least 0.5% of the displacement volume and at most 3.5% of the displacement volume. a stator body having an internal cavity defined by two axially spaced apart end walls and a peripheral wall extending between the end walls, the cavity having an epitrochoid shape defining two lobes; a rotor body having three circumferentially spaced apex portions, the rotor body being engaged to an eccentric portion of a shaft to rotate and perform orbital revolutions within the cavity with each of the apex portions remaining in sealing engagement with the peripheral wall and separating three rotating chambers of variable volume defined in the cavity around the rotor body; an insert (34; 134; 234) in the peripheral wall of the stator body, the insert (34; 134; 234) having an inner surface (66; 166; 266) bordering the cavity; an ignition element having a tip received in the subchamber; and a main fuel injector extending through the peripheral wall and having a tip communicating with the cavity at a location spaced apart from the insert (34; 134; 234); characterised in that the insert (34; 134; 234) is made of a material having a greater heat resistance than that of the peripheral wall, and has a subchamber defined therein, the subchamber communicating with the cavity through at least one opening defined in the inner surface (66; 166; 266) and having a shape forming a reduced cross-section adjacent the opening; the ignition element is received in an ignition element hole defined in the insert (34; 134; 234); by further comprising a pilot fuel injector having a tip received in the subchamber; and in that the volume of each chamber varies between a minimum volume and a maximum volume with a difference between the maximum volume and the minimum volume defining a displacement volume, the subchamber having a volume of at least 0.5% of the displacement volume and at most 3.5% of the displacement volume.