Sport V-twin
maybe
But then again, what does GSXR stand for? It may just be a model name.
Pulled from wikipedia: GS - Gran Sport, used to indicate a road going Suzuki standard motorcycle, the only model that still uses this designation in the Suzuki line up is the GS500.
XR - eXperimental Racing. Designation added to GS for Suzukis road legal race replica motorcycles thereby creating GSXR.
There are additional suffixes added to the GS "road going" moniker such as GSX (just Gran Sport eXperimental) for the Katana motorcycles or GSF (the F stands for something in Japanese that I can't remember but generally indicates a sporting but not race replica trim) for the Bandit motorcycles. To be noted, the Hayabusa is technically not a GSXR but some hybrid between the that and the Katana given it's model moniker GSX1300R.
Also to be noted, Suzuki's non-road legal race bikes are coded as XR for just eXperimental Racing.