Lots of things to match up:
Wheel spindle diameter(s): the ends of the K spindle might not match the bores in the bottom of the fork legs/or the GSXR spindle (if you use that instead) might not match the diameter of the ball races in the K wheel. A bespoke spindle, or boring/sleeving the fork legs is required.
Wheel spindle length/axle spacers: the K axle spacers might not be correct for the GSXR fork spacing. Bespoke/modified spacers are required.
Disc diameter: unless the K discs are the same diameter as the GSXR discs, then you'll need adaptor brackets to line the calipers up radially.
Disc offset/spacing: this is how far apart the discs are spaced axially. Assuming that you're already signed up for a set of caliper mounting adaptor brackets in order to achieve radial alignment, then the disc offset can be catered for in the adaptor brackets. If you're lucky, and you don't need adaptor brackets to move the calipers radially, then you have the option of placing spacers between the disc and the wheel mountings in order to achieve this axial alignment. Alternatively, you can machine the disc mounting posts, or the calipers mounts on the forks.
Note that when you are locating the caliper, it must clear the wheel spokes and, ideally, be removable with the wheel in place.
The above stuff is straightforward, but requires access to a sharp pencil and a machine shop. I'm not aware of any off the shelf adaptors or stuff, but you can sometimes get lucky with standard parts. I'm told that a GSXR wheel can sometimes fit straight in to a set of those forks.....
Edit, if you want to post some dimensions up here, then you'll get lots of advice from us K people. Take it in stages - first thing to settle is what wheel spindle to use