Same problem here, but I found a solution (or at least a workaround) that might work:
Using the AutoHotkey utility and this script, I was able to get the keyboard shortcut to work even on my Finnish layout:
#InstallKeybdHook
Numpad1 Up::
Send {vk5Bsc15B Down}
Send {vkC0sc029 Down}
Send {vkC0sc029 Up}
Send {vk5Bsc15B Up}
return
Now, every time I press (or actually release) the NumberPad 1 key, Groupy will switch to the next tab.
Now, if Groupy got a similar shortcut for stepping backwards (like using Shift+Alt-Tab), switching between tabs with the keyboard would become actually useful!