show the flag

(literally) To display the flag of one's country, especially as an expression of patriotic pride.

(idiomatic) Of a naval vessel or military force, to identify itself by displaying the flag of its country of origin, especially in order to establish an authoritative presence and to exert diplomatic or political influence.

(idiomatic, by extension) To represent one's country or some other group in a manner intended to suggest the authority or importance of that country or group.