Your kitty needs to play to develop his natural instincts. Join their games and you will create bonds that will last a lifetime. Normally, it is primarily his mother who is responsible for stimulating his behavioral development, but as an adoptive mother, your role is also important. So take the time to play with him.
To start, buy him some toys like a stuffed mouse or a ball - anything he can play without risk of injury (avoid objects that he can easily swallow). Or get creative, a simple ball will bring hours of fun. Another good idea is to hang something from a string and move it around so that he tries to catch it. But make sure he doesn't bite or swallow the string after playing.
Just look for encouragement
When your kitten plays with you, he is reviving the natural instincts that his ancestors had in nature. Play helps him tone his muscles and improve his circulation. In fact, it is excellent.
Kitten always follows his hunting instincts and have a natural urge to roam. Even if he like the routine and the security of your home and territory, his senses need stimulation. Otherwise, he can become nervous and aggressive. If he overdoes it, try to divert his aggressiveness towards a toy (never offer your hand as an alternative).
Wake up the hunter and not the fighter
Playing with your kitten is the best way to keep him calm. Anything that is good for hunting and scratching is perfect. Tie a ball of paper to a string and drag it around the room and over furniture. He will want to hunt it down right away.
Your kitty can learn a lot by playing with you. By creating different situations, you can let him know that certain behaviors are not acceptable, and if he has just come home and is still shy, this is a great way to get him used to his new surroundings.