。
That's acting like nobody else is around.
Literal
[yoji-傍若無人] [possessive-の] behavior [assertion-だ] [tag-ね]
傍若無人 is a 四字熟語 (four-character idiom) literally reading '(acting) as-if (there were) nobody beside (you)'. Used to scold arrogant, rude, or inconsiderate behavior that ignores others' presence. 振る舞い is a refined word for 'behavior/conduct' (from 振る舞う, to act/behave). The sentence-final ね invites the listener's agreement.