If I leave my motorcycle for a few weeks and do not fire him up, I get a little bit of drag when I engage first gear for the first time. This clears up as the bike warms up. It sounds like you have a bit more going on here; is the clutch and cable suspect at all? You can try and adjust up any play in the cable.Allow the engine time to warm up and operate the clutch lever and hold it in for a while repeatedly; the plates could be sticking too? Other than advising the obvious like strip the clutch and inspect or get the gixxer to a qualified mechanic; I am sure there will be more snippits of advice to follow
