Here's the preamble to
COPYING, included with the kernel source:
NOTE! This copyright does not cover user programs that use kernel
services by normal system calls - this is merely considered normal use
of the kernel, and does not fall under the heading of "derived
work". [...] note that the only valid version of the GPL as far as
the kernel is concerned is this particular version of the license
(ie v2, not v2.2 or v3.x or whatever), unless explicitly otherwise
So, if you want to create your own operating system userland from the ground up, then you can license that part however you like. You can then distribute the whole thing together, and the kernel will be licensed as the kernel is and your userland pieces licensed the way they are. This is not uncommon, since various proprietary systems use the linux kernel (although they would often include other open source pieces too, I think).
What you cannot do is distribute the whole thing together claiming your license applies to the included kernel (unless your license is GPL compatible).