A turbocharger, comprising: a compressor; a turbine comprising a turbine housing having a turbine wheel disposed therein, the turbine housing defining an annular chamber surrounding the turbine wheel for receiving exhaust gases from an internal combustion engine, and an axial bore (!35) through which exhaust gases are discharged after passing through the turbine wheel; a three-way valve housing comprising an inlet, a first outlet, and a second outlet, the inlet and the first and second outlets being connected to a valve chamber defined by the three-way valve housing, the valve chamber defining a cylindrical inner surface about a valve chamber axis, the first outlet having a first circumferential width and the second outlet having a second circumferential width; the turbine housing further defining a turbine feed passage connected between the first outlet and the annular chamber, and a bypass passage connected between the second outlet and the axial bore downstream of the turbine wheel; a rotary valve member disposed in the valve chamber, the rotary valve member having an open end and a closed end opposite to the open end, with the open end adjacent to the inlet of the three-way valve housing, wherein the rotary valve member and the three-way valve housing form a valve having an inlet defined through the inlet of the three-way valve housing and the open end of the rotary valve member, the rotary valve member being rotatable about the valve chamber axis between successive first, second, third, and fourth rotational positions, the rotary valve member comprising a hollow member having an outer wall defining a cylindrical outer surface confronting the cylindrical inner surface of the valve chamber, the outer wall defining a valve member outlet comprising an opening through the outer wall, the valve member outlet having a third circumferential width that is large enough to span across all of the first circumferential width of the first outlet plus a portion of the second circumferential width of the second outlet, wherein the first and second outlets and the valve member outlet are configured and positioned such that in the first rotational position of the rotary valve member, the valve member outlet overlaps all of the first outlet while the outer wall closes the second outlet, in the second rotational position the valve member outlet overlaps all of the first outlet and overlaps partially with the second outlet, in the third rotational position the valve member outlet overlaps partially with the first outlet and overlaps all of the second outlet, and in the fourth rotational position the valve member outlet overlaps all of the second outlet while the outer wall closes the first outlet. a compressor; a turbine comprising a turbine housing having a turbine wheel disposed therein, the turbine housing defining an annular chamber surrounding the turbine wheel for receiving exhaust gases from an internal combustion engine, and an axial bore (!35) through which exhaust gases are discharged after passing through the turbine wheel; a three-way valve housing comprising an inlet, a first outlet, and a second outlet, the inlet and the first and second outlets being connected to a valve chamber defined by the three-way valve housing, the valve chamber defining a cylindrical inner surface about a valve chamber axis, the first outlet having a first circumferential width and the second outlet having a second circumferential width; the turbine housing further defining a turbine feed passage connected between the first outlet and the annular chamber, and a bypass passage connected between the second outlet and the axial bore downstream of the turbine wheel; a rotary valve member disposed in the valve chamber, the rotary valve member having an open end and a closed end opposite to the open end, with the open end adjacent to the inlet of the three-way valve housing, wherein the rotary valve member and the three-way valve housing form a valve having an inlet defined through the inlet of the three-way valve housing and the open end of the rotary valve member, the rotary valve member being rotatable about the valve chamber axis between successive first, second, third, and fourth rotational positions, the rotary valve member comprising a hollow member having an outer wall defining a cylindrical outer surface confronting the cylindrical inner surface of the valve chamber, the outer wall defining a valve member outlet comprising an opening through the outer wall, the valve member outlet having a third circumferential width that is large enough to span across all of the first circumferential width of the first outlet plus a portion of the second circumferential width of the second outlet, wherein the first and second outlets and the valve member outlet are configured and positioned such that in the first rotational position of the rotary valve member, the valve member outlet overlaps all of the first outlet while the outer wall closes the second outlet, in the second rotational position the valve member outlet overlaps all of the first outlet and overlaps partially with the second outlet, in the third rotational position the valve member outlet overlaps partially with the first outlet and overlaps all of the second outlet, and in the fourth rotational position the valve member outlet overlaps all of the second outlet while the outer wall closes the first outlet.