How to mirror limb movement

So I'm trying to create an application which will be used with stroke victims, emulating the effects of a mirror box http://en.wikipedia.org/wiki/Mirror_box

I'm applying movement data to a character, but I want to ignore the right arm and have the left arm's movements be mirrored onto the right arm.

Each set of movement data comes in as a set of quaternion based rotations, which are applied to the relevant limb's transform.

How would I go about changing the left arm's quaternions to be rotated about the body so that they can be applied to the right?

Thanks for any help, Mitch