How is it that a Sharingan can work when it's been transplanted? If the various "superpower" ninja traits are considered "blood traits," how is it someone like Kakashi, who is in no way related to the Uchiha clan, can use the Sharingan Eye technique? 

More fully: would transplanting work on any bloodline trait power? If someone had a bloodline trait that worked on arms, could they just transplant their arm onto another person and then there would be two people with that technique?
Let's disregard the fact that eyes in Naruto are considered less difficult to work with than PnP displays. (Rin did it in a cave, without any medical supplies, in a couple of seconds, and it just worked)

Your eyes contain your DNA, so our (the Uchiha) eyes contain the already awakened Sharingan, it's written into the DNA.

It also has the genetic information allowing you to activate the techniques the eye holds (including Mangekyo).