The Shi'ar Enlightenment Church is a religious sect. The Church's dogma is said to have been created from alien knowledge that was granted to them from an ability to communicate with the Phoenix Force.
The Shi’ar Enlightenment dogma holds that the Phoenix was once an entity of creation, travelling the universe changing worlds at its whim, and always for the better. However, the Phoenix had created beings on the worlds it encountered. These beings grew to resent the Phoenix and covet its power, wishing to use it to control their own destinies. They amassed a great army, bringing together a hundred civilizations. The war with the Phoenix lasted a thousand years and cost the alien alliance many lives. In the end, the Phoenix was defeated. The alien alliance could not destroy the Phoenix, so they constructed a special prison around it, a cage that would be powerful enough to contain it.
The Shi'ar adherents believe that the alien alliance created the planet Earth around the Phoenix to serve as a prison. They believe that the Phoenix resides at the molten core - or perhaps, is the molten core of the Earth. Long after the civilizations of the alien alliance had become extinct, life began to form and evolve on Earth. The Phoenix detected life on Earth, and began to aid in its development. They believe that the leaps and bounds humans experienced in evolution were shepherded by the Phoenix's influence.
The first adherents of the Shi’ar Enlightenment claimed to be able to communicate directly with the Phoenix, though this art has been lost through the years. They created various tomes containing the contents of these communications, which they passed down through the ages. The tomes are the basis of a philosophy of rebirth and self-improvement, which makes up the Shi'ar belief system. The Phoenix also communicated a prophecy: That a mortal would, one day, host the entity, and eventually allow it to be reborn. This would free the Phoenix to roam free once again and bring about a utopia for all the denizens of the universe.
Several centuries ago, a group of the Shi'ar, calling themselves the Hellfire Club, split away, seeing the Phoenix as a being of destruction. The Shi'ar claim that the Hellfire Club twisted their philosophies and doctrines to their own agendas, changing the interpretation for their own ends.
Finding the Avatar
After the formation of the X-Men, the Shi'ar Church learned of the young mutant, Jean Grey, and believed her to be the avatar and/or host of the Phoenix. The Majestrix of the Church, Lilandra, contacted Charles Xavier, Headmaster of Xavier's School for Gifted Youngsters, offering him funding in exchange for permission to test Grey. Xavier agreed only when Grey consented to the testing. Lilandra and her assistant Gerald Lavine performed the tests using their tomes, which contained scientific data to assist in discovering the identity of the host. However, the tests resulted in the Phoenix force seemingly manifesting. The Phoenix threatened to kill Lilandra and only the timely intervention of Xavier returned Grey to normal. Afterwards, Lavine revealed that the tests showed that Grey's blood contained none of the properties enumerated in the tomes and that she was not the host of the Phoenix. Lavine claimed that Grey’s parents were members of the Shi’ar Church and that she must have fixated on the symbol of the Phoenix as a means to come to terms with her powers. However, Lavine was actually a member of the Hellfire Club, and he was hiding the fact that the analysis had revealed that Grey's blood was an exact match.
Lilandra, unaware of his allegiances, placed Lavine in Xavier's school ostensibly to aid Grey in her search for answers. Instead, Lavine spied on Grey under the orders of Shinobi Shaw, another member of the Hellfire Club. Eventually, when Shaw visited the school, he and Gerald attacked Grey in an attempt to capture her. This failed, as the Phoenix manifested, almost killing both Shaw and Gerald. Afterwards they were taken into police custody and Lilandra was forced to face that fact that Lavine had betrayed her. 
Unlike their Earth-616 counterpart, the Shi'ar are not an alien race, they are a human religious sect.
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