The Kharijites I hear were the ancient "Taliban" so to speak.  They were against the decadence of the Caliphs and wanted a more purer form of Islam and were hated by the establishment.

What is the story behind this movement?  Anybody know?

The Kharijites were actually formed during the time of Caliph Ali. In the late times of Caliph Osman, conflicts started among different power groups among Muslims.

Later Caliph Osman was murdered and Caliph Ali,who was the cousin of prophet Mohammad, came on as the new caliph, and rebellions started to begin. First, Aishe, the wife of Mohammad, together with close companions of the prophet named Talha and Zubeir, formed an army and fought with Caliph Ali(Battle of Cemel it is called in Turkish, it means Battle of Camel. It is named in that way because Aishe joined the war on her camel).Later, the predecessors of later Umayyad Empire, under the leadership of Muawiyah(son of Ebu Sufyan,a Muslim commander who was the commander of Mecca people before), the founder of Umayyad Empire rebelled against Ali. That was one of the reasons Ali moved the capital of Islamic Caliphate to Khufah, to form a new base for himself. And Muawiyah was the governor of Damascus.

Anyway, the conflict had mainly began to pass on between Caliph Ali and Muawiyah,later two sides fought, and Event of Arbitration(When he understood he was gonna lose, Muawiyah had ordered his soldiers to put pages of Qur'an on their pikes, so the army of Caliph wouldn't be able to attack them, and later two arbitrators from each sides were chosen to solve the event, but Muawiyah's tricks had intervened and arbitration decided for Muawiyah) had happened.

After that event, the Muslim world of that time certainly divided into two. The ones who supported Caliph, the ones who supported Muawiyah. And another third group, who was displeased with both of them, was formed under the name of Kharijites and opposed both of them.

In year of 661, the Kharijites arranged a plan to kill both Ali and Muawiyah, and Muawiyah's army commander, Amr Ibn As. Muawiyah and Amr Ibn As saved themselves coincidentially at the last minute, but the Caliph was unfortunately killed.

After this event, Umayyads took on with the empire, and killed Ali's sons, Hasan and Hussein in Kerbela(In today's Iraq), and that event pitifully caused the Islamic world to be divided into two as Sunni and Shiite fractions.

So Kharijites have a lot of share in that division and conflict..

the People who killed Caliph Uthman were the same group fromw hich the Kharijites (Khawarj) came from.

and AL Hasan was not killed by the Umayyads.

i dont think they wanted to return to the ideal days of muslim community.

they wanted control and a pupet caliph who obay them and they being able to replace him anytime they want.

at the beginning yes.