Ok, since I promised detailed instructions:
Arch packages are just
.tar.gz files, so I downloaded and unpacked the kernel from the same URL which is used by Arch's package manager.
Inside the archive, there are
usr directories, which contents I copied inside the corresponsing directories on my hard disk.
Then I looked into
.INSTALL file and realized that I need to run
depmod -a $KERNEL_VERSION
which supposedly "generated
modules.dep and map files".
Then I added the kernel to the GRUB boot menu as described here, although as I remember the file I edited was different.
In my tests, the machine booted 5 seconds faster with the new kernel and used slightly less RAM than with stock Ubuntu kernel.
And it was fun :)