You can find the complete story in Insufficent Data, which is a collection of my favourite short sci-fi stories.
This is Planet Schwarzenegger
What if you could become a copy of anybody you love or admire? This Is Planet Schwarzenegger is a science fiction adventure set in the year 2373, when human civilisation has spread across the arm of the galaxy. Genetic manipulation has greatly advanced, allowing people to live out their fantasy lives. Some humans choose to become replicas of their idols. The rich, the famous and historical figures are popular choices. Richard Quaid, an Arnold Schwarzenegger replica, realises his life dream to travel to Planet Schwarzenegger - a theme-world devoted to honouring the great Austrian bodybuilder and actor. However when he gets there he finds finds he has become ensnared in mysterious series of events. Arnold replicas have been disappearing - and Quaid may be the next to be terminated! Quaid must solve the mystery and get to the bottom of the terrible secret of Planet Schwarzenegger - before it's too late.
