Ask HN: How do you manage a project you don't believe in?

As head of technology I just received a new project, conceived only by the CEO. It’s coming to me “ready to be built”. The project is wrong, there are a lot of bad ideas and it won’t work business wise. Usually I have full control on projects but not this one. I did meetings to alert many board members. But it’s apparently too shiny on paper. I have to pursue, set up the team and use my skills to make it work "as it".

How do you manage a project and do top quality work, when you know everything will go to the trash at the end ?