Kiba, which aired in 2006-2007?
In a dystopian future, two friends dream of freedom... and gain more than they bargain for! Hothead Zed is on the run from the authorities, while his brainy pal Noah struggles with his own battered body. Both find a magical world that seems to offer escape and power undreamed of. Join Zed and his powerful, rebellious spirit Amir Gaul on their search for the ultimate power. It's a force that can save the world—or destroy life as we know it. This is the world of KIBA! Where you must harness the power within and fight with all you got!
Here's the lead character, Zed. White-haired, has three "shards" on his arm:
And here is Roya, who wears a crystal on her chest, and her spirit Afkareru, who does look a bit like a jellyfish:
I found it by searching this site for
[story-identification] anime arm is:q which returned, among others, Anime with character who has markings/balls on his arm that allow him to operate weapons