Radiohead could be pegged as a band to make complicated music, not my words, and covering those type of tunes with a jazzy twist might be the challenege that these artists are after. Don't that band G4 transform a Radiohead song into something a little more digestable for the radio-friendly masses?

One reason would be that Radiohead are almost universally artisically respected so doing a Radiohead cover is pretty safe bet artistically and is often a good way to get peoples attention. Its not just jazz, there's tons or Radiohead covers from all genres and of varying quality out there. Some are a little gimmicky and opportunistic, for example The Darkness do a hair metal cover of "Street Spirit", which was given away free as an MP3 and used to generate a lot of the initial publicity for the band before they even had released an album. Others Radiohead covers are great and reflect a real love of the source material. Possibly the best Radiohead cover is when I saw Gillian Welch live and she did a cover of "Black Star" The other reason Radiohead appeal to Jazz musicians is as Gar said, they are a band perceived as making complicated music and are much loved by "serious" musos, which are generally the same kind of musicians who like to play Jazz. Radiohead often use unusual chord structures and time signature changes that aren't commonly found in rock music. Theres also the fact that Kid A/Amnesiac take an influence from the whole Warp Records IDM thing with unusual, complex and layered beats and rhythms. The poster boy for Warp is of course Aphex Twin who coincedentally is also covered by a lot of Jazz musicians too.

Another reason could be that Radiohead are big into jazz themselves. For a while it looked like the band couldn't give an interview without mentioning The Art Ensemble of Chicago.

for me its too reasons: the most popular band of any era will always have interesting covers done of their music. Radiohead and jazz fans would probably both consider themselves musically educated. thus a match made in the blue note marketing department!

I think it's the way their songs are constructed and/or written. If they are big into jazz as stroller said, there's probably an element of jazz inherent in the music anyway, so it probably converts easily, as well as creating a good sound.