The invention relates to a turbine engine (2) compressor shroud, comprising: first and second sections (130, 230) and respective flanges (131, 231), the flanges (131, 231) making it possible to hold the two sections (130, 230) together, the first section (130) comprising a cylindrical surface (137) forming a seat for an actuating device (136, 140, 166, 168, 170) for orienting stator blades (126), characterised in that the first shroud (130) comprises a tubular wall (132) axially overlapping both flanges (131, 231) and said cylindrical surface (137) is an outer surface of the tubular wall (132). The invention also relates to an assembly with the shroud (130, 230), the blade (126) and means (140) for actuating the orientation of the blade (126), the shroud being produced using the kit described above. The invention finally relates to a method for assembling a compressor with such an assembly.