What should be done in a case where the shliach tzibbur when davening chazaras ha'shatz makes a mistake and instead of saying "HaMelech HaKodesh" during Eseres Yamei Teshuva he says "HaKel HaKodesh". Normally the halacha by a yichud if the person has already gone further in Shemoneh Esrei and realizes this mistake they have to go back to the beginning of the Shemoneh Esrei. By a shliach tzibbur if this was realized after a point where it cannot be corrected must the shliach tzibbur start over again chazaras ha'shatz?
One who errs in this regard must start over from the beginning (Shulchan Aruch, OC 582:1). The Beit Yosef implies that this applies to a sh'liach tzibbur, as well (OC 582:2). The Sha'arei T'shuvah, quoting the Z'kan Aharon (§ 6), rules explicitly that the sh'liach tzibbur must return to the beginning, and must repeat k'dushah, as well (OC 582:1).