What is up with "my" cat?

We recently moved into a nice little area in the woods. The house gets hot, so once day we left the door open and this stray cat just comes walking in like it's ours. He was friendly, stayed in for a few hours, then left for the night. Now this is a new ritual for us: wake up, let him in the house, and then at night let him out. He shows up every day like clockwork.

But something about him is, well, off. He doesn't look... "right" for a cat. He looks like a wild animal. He has the same fur tuffs on the sides of his face and he has long tuffs of hair the spike off the tips of his ears. His eyes are this really weird blue-aqua color that I've never seen before, and he is stocky with paws that are 2X the size they would be on a regular cat. He only weighs maybe 15 pounds, but his paws are HUGE. He isn't a maincoon, I'm sure of that... He doesn't look like any cat I've ever seen. His fur is really thick and plush... is he some kind of bobcat mix? can that happen?