barrack

(BAR-uhk, the first syllable is the same as in barrel)

verb tr., intr.: 1. To shout in support: to cheer. 2. To shout against: to jeer.
noun: A building used to house soldiers.

The verb sense of the word is perhaps from Northern Ireland dialectal barrack (to brag).
The noun sense is from French baraque, from Italian baracca or Spanish barraca (hut, tent).

"Raphael Clarke said: Every kid wants to play for the team they barrack for."
Lyall Johnson; Clarkes Praise the Saints; The Age (Melbourne, Australia); Nov 23, 2003.

"During the debate, then Socred leader Rita Johnston and NDP leader Mike Harcourt were barracking away at each other about corruption."
Ross Howard; TV Debate; The Globe and Mail (Toronto, Canada); May 16, 1996.