I want to publish story on the behalf of the user with app owned object which is hosted on the web. how can it be done with v4 of the facebook android sdk?
I can see example of it for older version of the sdk here: Publish story with web hosted object
How can it be done for V4?
Checkout the ShareOpenGraphContent.Builder and ShareOpenGraphAction.Builder classes to construct your OG objects and actions. If you're hosting your own objects, then you might only need to use the ShareOpenGraphAction.Builder.
See also the Scrumptious and RPS sample apps that gives examples on how to create the OG actions and share them through either ShareDialog or ShareApi.