Why does Tyler Durden leave the Narrator taking his suitcase?

After the crash Tyler takes his suitcase and leaves to set Project Mayhem in motion so it can continue without him.

He leaves sleeping Jack in the room (i.e. takes control of his body), gives specific instructions to everyone in the Paper Street Soap Company building and in other Fight Clubs around the country (hence the suitcase with tickets etc.) so that when he goes back and relinquishes Jack's body, Jack can't do anything to stop it.

That's why later we see Jack walking aimlessly around the house where everyone in was doing their part of Project Mayhem (Jack calls it "controlled chaos" or something like that). Only after Bob's death he decides to follow Tyler's trail and realizes Tyler had given specific instructions all around the country - to deny his existence of the Clubs, to spread false information about Tyler Durden, to cut balls of everyone trying to stop it (even including Tyler himself) etc.

Similarly, later after Tyler shows up in the hotel (and he does that because Jack spoke about Tyler to Marla, against his triple promise) and Jack learns the truth (that they are sharing the same body), Jack again loses his consciousness and wakes up several hours later with a phone in his hand, because Tyler has used his body to make calls to give Project the green light.