Place the papaya, sugar and water in a food processor. Puree until smooth. Place the mixture in a pot and simmer 2 to 3 minutes to dissolve the sugar. Strain the mixture through a fine sieve, using a whisk to get as much juice out of the pulp as you can. Combine the strained mixture with the lime, orange and pineapple juice. Chill well. Serve in ice-filled glasses. Garnish with papaya and lime wedges.