Mechanim animation problem: Why aren't my character's hands moving?

I'm trying to bring a humanoid character (modelled & animated in Cinema4D) to life in Unity 4. I've created a Humanoid Avatar for him; all the mandatory and optional bones have been set up properly (even both hands with every single finger bone) and I've imported my walking animation.

If I drag the character into a scene he has already assumed the right pose for the first frame of the walking animation. Note how the hands are slightly closed just like they should be:

But if I set up the walking animation using an Animation Controller and play the scene the animation starts playing perfectly fine except for one detail: The hands are not animated, they are open just like in the T-pose:

I have no idea why this happens. The animation's Body Mask and Transform Mask both cover the whole body including hands. The Animation State is in the Base Layer so there is no masking involved.

Any ideas why this happens?