The researchers in question are named Susumu Tachi, Masahiko Inami and Naoki Kawakami. They work for the University of Tokyo and their first announcement was around 2003 !

That's exactly what it is....a projection on a special material. So it's not just a jacket by itself, you need to project the background image onto it by using a camera to record the background at the same time.

there is a theory behind in physic that you can bend the light wave so it doesn't reflect off the object, so making it really hard to see the object

Ever tried to stand in front of a projector? Thats the big shadow behind. Give the person a very reflective coat. Then light face and hands from the sides. Voila magic.

It's actually real, the cloaks are made of thousands of reflecting spheres that reflect all the light around them. They're still prototype. But a Google search can find some cool shit