Xen users - Mar 2012 - Illegal instruction with certain applications

Hello, I''m a beginner with Xen, in particular on the Dom0 side (used it
for a while in my VPS as DomU).

I''m running Linux 3.3.0, with Xen enabled. I''m using Xen
4.1.1.

This is my GRUB2 configuration:

menuentry ''Xen'' {
        set root=(hd0,msdos1)
        multiboot /xen.gz placeholder
        module /kernel-3.3.0-1 placeholder
        module /custom-init-1
}

Everything seems to work fine until I try to start X11 or
wpa_supplicant, as they die with a SIGILL (Illegal instruction). If I
boot the same kernel without the hypervisor everything works as usual.

My CPU is a Intel(R) Core(TM) i7-2820QM, if it matters.

Am I missing something or could this be a bug?

Thanks in advance!