a pompon (puff or ball as for decoration for cheerleading)

support / cheering

aid, back up, support / cheer, root for

(formal) Female third-person singular pronoun; she, her, girlfriend

(colloquial) a girlfriend (a female partner in a romantic relationship)

(literary) they (about women or girls)

to shake; (of a hand or flag) to wave; (of a tail) to wag; (of a baseball bat) to swing; to move something back and forth in a circular motion

swing, wield, flourish, wave, shake

assuming the air of, acting like it (when one is not)

cheer group