An apparatus for unfolding a rolled-up, elongate hollow body provides for stabilizing the unfolding body in a transition region. The hollow body has a closed cross-sectional profile. The unfolding mechanism has a winding core on which the hollow body is rolled up and compressed in a first state, and, by rotation, transfers the hollow body to an unrolled and unfolded second state. The hollow body is guidable between an outer fixing element positioned outside the hollow body and an inner supporting element which lies against an inner wall of the hollow body. The inner supporting element and outer fixing element interact in a form-fitting and/or force-fitting manner for axial positional fixing of the inner supporting element without a directed mechanical connection.