(most of the fighters are not Iraqi but Islamic jihad fighters
Totally and factually wrong.
The Iraqi insurgency is composed of at least a dozen major organizations and perhaps as many as 40 distinct groups. These groups are subdivided into countless smaller cells. According to the Chief of the British General Staff, General Sir Richard Dannatt, speaking in September 2007,
The militants (and I use the word deliberately because not all are insurgents, or terrorists, or criminals; they are a mixture of them all) are well armed – probably with outside help, and probably from Iran. By motivation, essentially, and with the exception of the Al Qaeda in Iraq element who have endeavoured to exploit the situation for their own ends, our opponents are Iraqi Nationalists, and are most concerned with their own needs – jobs, money, security – and the majority are not bad people
Because of its clandestine nature, the exact composition of the Iraqi insurgency is difficult to determine, but the main groupings are:
* Ba'athists, the armed supporters of Saddam Hussein's former regime, e.g. army or intelligence officers;
* Nationalists, mostly Sunni Muslims, who fight for Iraqi self-determination;
* anti-Shi'a Sunni Muslims who fight to regain the prestige they held under the previous regime (the three preceding categories are often indistinguishable in practice);
* Iraqi Sunni Islamists, the indigenous armed followers of the Salafi movement, as well as any remnants of the Kurdish Ansar al-Islam;
* Shi'a militias, including the southern, Iran-linked Badr Organization, the Mahdi Army, and the central-Iraq followers of Muqtada al-Sadr
* Foreign Islamist volunteers, including those often linked to al Qaeda and largely driven by the Sunni Wahhabi doctrine (the two preceding categories are often lumped as "Jihadists");
* Various socialist revolutionaries (such as the Iraqi Armed Revolutionary Resistance);
* Nonviolent resistance groups and political parties (not part of the armed insurgency).
http://en.wikipedia.org/wiki/Iraqi_insurgency
AQ in Iraq, and foreign fighters, make up perhaps 5-10 % of the insurgency, and are not supported by Iraqi national in any real way.
The overwhelming majority of insurgents are Iraqi nationals fighting what they see as an army of occupation, for various motivations.