Connive

(Courtesy of Merriam Webster Online)

connive \kuh-NYVE\ verb

*1 : to pretend ignorance of or fail to take action against something one ought to oppose
2 a : to be indulgent or in secret sympathy : wink b : to cooperate secretly or have a secret understanding
3 : conspire, intrigue

Example sentence:
Did the professor connive at the cheating that was going on during the exam, or was he unaware that it was happening?

Did you know?
"Connive" may not seem like a troublesome term, but it was to Wilson Follett, a usage critic who lamented that the word "was undone during the Second World War, when restless spirits felt the need of a new synonym for plotting, bribing, spying, conspiring, engineering a coup, preparing a secret attack." Follett thought "connive" should only mean "to wink at" or "to pretend ignorance." Those senses are closer to the Latin ancestor of the word ("connive" comes from the Latin "connivēre," which means "to close the eyes" and which is descended from "-nivēre," a form akin to the Latin verb "nictare," meaning "to wink"). But many English speakers disagreed, and the "conspire" sense is now the word's most widely used meaning.