Peel the ginger and finely grate. Peel the lime and orange with a peeler. Squeeze the lime.
Bring 1 liter (approximately 4 cups) of water to a boil with the sugar. Add the ginger and cook for 1 minute. Add the lime and orange peel and lime juice. Add the ginger syrup and cool. Refrigerate for 24 hours.
To serve, pour the ginger beer through a fine sieve and serve with star anise in glasses.