Putin is making a fool out of Abe but Abe doesn't know it.

http://edition.cnn.com/2016/12/15/asia/putin-abe-japan-arrival/

The japanese government has been whitewashing its WW2 history till now and very few people know the true account of these kuril islands anymore.

These kuril islands belonged to Russia and Russia let Japan have them in exchange for non-invasion from the Japanese during WW2.  However, Japan attacked Russia after taking the kuril islands.  Therefore, Russia took back the kuril islands after the end of WW2 because Japan didn't honour the agreement.

Abe still harbours the wishful thinking that Russia will return the kuril islands but Putin won't return them back to Japan as Japan reneged its promise in WW2.  Putin is just playing Abe for this episode.