The goal of this enhancement is to build reproducible modules-qemux86.tgz tarballs for:

$ MACHINE=qemux86 bitbake core-image-minimal


The resulting tarballs of this build are placed in the folder <builddir>/tmp/deploy/images/qemux86

Repeating the build in a different folder will place the tarballs in:
<builddir-different>/tmp/deploy/images/qemux86

The build is deemed reproducible if the tarballs are binary identical.
This is rather simple, replacing the line in kernel.bbclass:

tar -cvzf ${DEPLOYDIR}/${MODULE_TARBALL_BASE_NAME} -C ${D} lib

with:

sde=$(get_sde)
tar -I "gzip -9n" --sort=name --clamp-mtime --mtime=@$sde -cvf ${DEPLOYDIR}/${MODULE_TARBALL_BASE_NAME} -C ${D} lib

But we should wait until we resolve:
https://bugzilla.yoctoproject.org/show_bug.cgi?id=12707

(Otherwise we would need to do some run-time checks for supported "tar" command line arguments)