Words related to *keue-
c. 1400, "a concave surface," from Old French concavit "hollow, concavity" (14c.) or directly from Latin concavitatem (nominative concavitas), from Latin concavus "hollow, arched, vaulted, curved," from con-, here perhaps an intensive prefix (see con-), + cavus "hollow" (from PIE root *keue- "to swell," also "vault, hole"). From 1570s as "state of being concave."
1610s, "a swindler;" 1650s, "anything intended to lead (someone) into a snare;" 1660s, "a lure employed in enticing game into a snare or within range of a weapon;" perhaps from Dutch kooi "cage," used of a pond surrounded by nets, into which wildfowl were lured for capture, from West Germanic *kaiwa, from Latin cavea "cage" (from cavus "a hollow" (from PIE root *keue- "to swell," also "vault, hole").
The first element is possibly the Dutch definite article de, mistaken in English as part of the word. If this is right, the later sense in English is the etymological one. But decoy, of unknown origin, was the name of a card game popular c. 1550-1650, and this may have influenced the form of the word.