In 2v2, can I play cards that say 'your base' to my friend's base?

Ruling: No, your friend's base is not your base. You cannot play cards that reference "your base" to your teammate's base.

Nuances:

• If you attempt to move a unit controlled by another player into your base, it just doesn't move (though this may be changed in the future so it goes to their base instead)
• Yasuo will receive errata to clarify that he moves friendly units to their controller's base