False flag
A false flag operation is a covert or underground operation intended to appear as though it were being carried out by other entities. The purpose is propaganda, to gain sympathy for the "attacked" and against the "attackers".
Nazi Germany carried out many such operations, such as the Reichstag fire, in order to gain popularity and cement its control on the government. Another notable one backfired on them, however, the Gleiwitz Incident (an "attack" on a Nazi radio operation by other Nazis dressed as Polish soldiers, which was itself nothing more than a short anti-German broadcast, made believable by the Gestapo's murder of a German who was sympathetic to the Polish, who was then dressed as a saboteur) would ultimately lead to World War II.