Updating this post because I'm watching Late Night With Stephen Colbert on July 20th, 2017. Chris was still playing the same instrument I wrote about back in 2012. Here is what I wrote about it back then.
If you saw Muse on Saturday Night Live (Oct 7th, 2012) playing the song, Madness, you may have noticed the bass player, Chris Wolstenholme, playing a very strange looking instrument that looked like a bass guitar with a back-lit touch screen which he used to play the notes.
It was a combination Misa Kitara Digital Guitar Synth Controller on the top and Status Graphite S2-Classic headless bass guitar put together like a double neck guitar.
Misa (misadigital.com) even has the music video for Madness which shows Chris playing JUST the Misa Kitara (not the mashup with the Status bass). So we know for sure that Misa acknowledges the use of the Kitara on the song.
And since Chris has a signature series bass with Status Graphite, we can be pretty darned sure his combo instrument on Saturday Night Live was, in fact, made up of a Misa Kitara and Status Graphite S2. [Update in 2020 - The Kitara has been replaced with the Misa "Tri-Bass Digital." And even that is showing as "sold out" on the Misa site.]
What the Kitara touchscreen thingy is doing is acting as a combination synthesizer and MIDI controller. There are internal synth sounds that you can select through the synthesizer engine.
And then you can apply any number of digital effects to those sounds. The "fretboard" on the neck of the Kitara has no strings, but rather 24 frets, each with a row of 6 buttons, each corresponding to a specific note. The default is that each note is what it would be on a guitar. But you can change those up however you like.
As a MIDI controller, you can connect any MIDI instrument or sound source you have to the Kitara, and trigger them with it, controlling your MIDI gear with the Kitara.
Both Misa and Status Graphite are being very tight-lipped about the dual instrument used by Muse on SNL, probably either because the instrument combo was cobbled together after-market, or is otherwise not available for purchase.
If you want a Kitara for your very own (minus the bass guitar hanging off the bottom;)), you may need to check on eBay for a used one, since they are apparently not being made anymore.
Find out more about Status Graphite here: http://www.status-graphite.com/