ПОД ЗНАМЕНЕМ чего rhetPrepPInvarthe resulting PrepP is adv
guided, driven by sth. : under (beneath) the banner of
in the name of.
Она (Анна Николаевна) шла в революцию под знаменем долга и жертвы, я - под знаменем моего свободного желания (Богданов 1). She (Anna Nikolaevna) had entered the revolution under the banner of duty and sacrifice, while I had joined it under the banner of my own free will (1a)