I'll have to be honest with you in that I don't know what the exact reaction is that makes your skin turn green when exposed to copper. But let me give you a little bit of background on what I know and maybe you'll be able to find it for yourself.

Copper, when exposed to certain chemicals, can form several different copper "salts" which are green. Now, your body is always secreting chemicals through your skin (in your perspiration, etc.). My guess, is that something from your perspiration (which you are always doing, not just when you're sweating during exercise!) reacts with the copper and is making one of these green salts. Two copper salts that I'm pretty sure are green are copper sulfate and copper acetate, but I don't know if these are the salts that are actually forming on your skin. I'm not sure if you know this or not, but the Statue of Liberty is actually made of copper, and at one time wasn't the green color it is today. It's turned green over the years due to exposure to the environment.

Again, while I'm not sure about this, there is some amount of sulfur in the air (sulfur can come from burning coal, for example), and "acid rain" is actually made up of sulfuric acid. My guess is that a copper sulfate has been formed to give the Statue its green appearance. I also wouldn't be surprised if there were additional salts as well that contributed to the color.