From an e-mail I just got:
you know?
"Let the Queen know of our gests," Antony instructs his men after a hard-won
victory on the battlefield in Shakespeare's Antony and Cleopatra. Great
deeds and heroic acts have been the stuff of gests since medieval days; in
fact, the word is more often associated with knights and heroes of old than
with modern adventurers. We may not be hearing about many 21st century
"gests," but we do frequently encounter other relatives of the word. "Gest"
traces to Latin "gestus," the past participle of the verb "gerere," which
means "to wage," "to accomplish," or "to act," among other things. That
Latin verb gave us stoutly enduring words like "gesture," "ingest," "jest,"
"register," and "suggest."

I've always spelled it as in "Beau Geste", story about French Foreign Legion
I so much enjoyed as a teen-ager.