Ties between the Jesuits and the Byzantine?

I am reading into Society of Jesus , seeking to uncover its parallels and differences with Orthodox Christianity. It is attested the Jesuit order was formed in France on August 15th 1534, by Ignatius de Loyola and approved by Pope Paul III in Rome on September 1540 [REF ] when presented with an outline; unable to uncover this outline, I'm interested in finding the extent in which the order had evangelized according to its Byzantine roots from this point in history on to this present day.