Radiohead didn't tour immediately after the release of their 2007 disc In Rainbows, but weeks after the album appeared online they did stream a series of in-studio webcasts heavy on the new material. They've never been a band to play many covers at their gigs, but one of these webcasts featured "The Headmaster Ritual" by the Smiths and an incredible rendition of "Ceremony" by New Order.
"Ceremony" began as a Joy Division track. It was one of the last songs Ian Curtis worked on before he committed suicide, and they performed it during their final concert on May 2nd, 1980. When the surviving members of Joy Division formed New Order a few months later, they revisited the track and cut a proper studio version. A few months later they recorded it yet again, this time with new member Gillian Gilbert on guitar. Fans have spent the last 30 years endlessly debating which one is the best version. Unfortunately, every known recording of the song by Joy Division is marred by inaudible vocals.
Radiohead wrapped up their 2012 world tour in Melbourne Australia on November 17th. They didn't break out "Ceremony" (or any other covers) during the course of the long tour.