Yes, this is something I am experimenting with. Currently, you can give artifacts and minerals to members of your legion, but this does not work like "gifts" in other games where you are essentially getting something for nothing.
With that in mind, here are the current list of things you can do for your legion:
* Share temporary locations of planets once per day
* Trade artifacts and minerals
* Guard legion planets
* Build on your legion's planets
* Repair your legion's disabled ships
And of course, theres more to come!