Teshuvah for all past sins on Yom Kippur:
The Teshuvah of Yom Kippur is an obligation for all. Even those that have not sinned, or have already done Teshuvah, must do Teshuvah on Yom Kippur. Although Teshuvah is a positive command that must be fulfilled irrelevant of Yom Kippur, nevertheless there is a specific Mitzvah of Teshuvah on Yom Kippur. Some explain this to refer to that those who have not yet done Teshuvah by the arrival of Yom Kippur, must do so on Yom Kippur. This however does not explain the wording of the Rambam that Yom Kippur is a day of Teshuvah for all, even those that have no sin. The Rebbe hence explains that Yom Kippur is a day that all Jews must repent for any sin he had in his lifetime. Meaning, even if one already did Teshuvah, he is to still do a further Teshuvah on Yom Kippur. Hence, since there is no man on earth without sin, every Jew repents on Yom Kippur.
 Likkutei Sichos 29 p. 203