What do you do after you defeat Groudon in Pokemon Ruby?

It depends on which move setup you have and what level your Pokemon is

like lets say you have a sceptile

and the moves you have are:

brick break (T.M. you find in Sootopolis)

leaf blade

rock tomb

and rock smash (H.M. you have after the first gym leader)

you would definitely be able to defeat him then

BUT:you would have to have a level 50 or higher

he is the most powerful wild Pokemon BEFORE the elite four