A game like cyberwars may work (if the graphics are clear enough) as a turn-by-turn, rather than real time mobile game.
not so sure about cyberwars, but Checker, Connect4, Reversi would surely work fine
Problem with online games is that the baud rate for mobiles is rarely above 4600-5800, and is prohibitively costly to keep uplinked.
I'm sendng just few bytes per second. (Main bandwith eater will be probably chat) Bandwidth is sure no problem for turn based game. (Costs probably IS problem

)
UMTS/3rd gen will be able to handle it, but then it'll jump past java based online games and straight thru to higher end codes (I would imagine).
Hm, java sure has big advantages, compared to other technologies. It's hard to predict which technology is going to win in the end.
Could be worth discussing though. Have a brother who does bus.dev. on mobile gaming for Nokia, will ask him what he thinks when he's next around.
Get a proposal drawn up & send it to me at
dogmarisk@hotmail.com - I'll pass them on to him.
Funny, I tried to get a job in Nokia two years ago, but my CV probably did not make it through Human Resources

I'm not sure what exactly I should/could discuss with your brother, because this idea is not new and such games surely already exist, but I'll send you email anyway.