An Etymological Dictionary of the German Language/Stauche
Stauche, f., ‘veil, sleeve, muff, mitten,’ from MidHG. stûche, OHG. stûhha, f., ‘the broad pendant sleeve on a woman's dress, kerchief, veil, cloth, apron’; corresponding to AS. stocu, ‘long sleeve, OIc. stúka. The Rom. cognate, Fr. étui (Ital. astuccio), ‘case,’ has been derived rom a Teut. *stûkjo. Teut. stū̆kô (stū̆kjo) is usually connected with a pre-Teut. root stū̆g; OLG. stûkan, Du. stuiken, ‘to pile up, push,’ and Lith. stùgti, ‘to look aloft.’