The GCC (EI) was founded in 1974 during the negotiations that led to the signing of the JBNQA. The GCC (EI) advocates for the Crees of Québec provincially, nationally and internationally. As a signatory of the JBNQA, the GCC (EI) sees to its application. It is composed of a Grand Chief and a Deputy Grand Chief elected by universal suffrage, and two representatives from each of the nine communities, including the band council chiefs. The head office of the GCC (EI) is located in Nemaska.

The goal of the GCC (EI) is to obtain self-government for the Crees. Most of the Cree public organizations, such as the Cree School Board and the Cree Board of Health and Social Services of James Bay (CBHSSJB), also work towards this goal. With the signing of the Agreement Concerning a New Relationship Between le Gouvernement du Québec and the Crees of Québec in February 2002 (the Paix des Braves), the GCC (EI) agreed that the Government of Québec shall treat the Crees as a nation and seek to obtain the same recognition from the federal government.