a cutting and transport roller and a process for cutting the material webs which rest on the peripheral surface of the cutting and transport roller . in so doing , the material webs are severed with the aid of a cutter , which is located inside the shell of the cutting and transport roller in its resting position and which exhibits at least one knife , which during the cutting process of the material web reaches through an opening in the shell of the cutting and transport roller . the cutting motion , which is executed by the cutting surfaces of the knife during the cutting process , exhibits rotary components , whereby the rotational motions of the knife run about an axis of rotation , which is either parallel or at an acute angle to a perpendicular line on the plane which is defined by the radial and axial coordinates of the cutting and transport roller .