Doubt with cross compiler

Hello everybody,

I have a doubt about cross compiles.
Normally, I use OSELAS toolchain to create my own cross compilers but I am not sure if cross compiler need use the same kernel that I going to use in embedded system or I could use a different one.
For example, I just create a cross compiler:
platform-i586-geode-linux-gnu-gcc-4.9.2-glibc-2.20-binutils-2.24-kernel-3.16-sanitized

But I am going to use a different kernel in my embedded system, kernel 3.6.11

any advice?

I have no idea what is that OSELAS, but I think any compiler can use any kind of kernel (not only the active one). It depends only the configuration of the build environment.