As with Pokémon Colosseum, you are capable of linking to your GBA Pokémon games for a variety of things. Below are their listings

Trading

Trading

Well the first thing is the trading from Pokémon XD to your GBA games of your fully purified Pokémon allowing for you to use them in your GBA Games

Battling

XD also has a Battle Mode. In it you can link up Pokémon Ruby, Sapphire, FireRed, LeafGreen & Emerald to battle. You can even use your XD team (as long as it has No Shadow Pokémon in it)
As in Colosseum you battle with your GameBoy and pick your attacks there. You can set up rules however you want such as level restrictions, item restrictions & Pokémon restrictions. You can even decide whether to mask Deoxys form or not, whether to show them all as Normal Form or to see them in their true game's forms
Once selected the battle begins. Be prepared to whoop your friends