Mention Cayman Islands to taxing authorities in any country and you'll probably be audited for the rest of your life...and rightly so.
Hope, too, that they don't change their laws and share info with other nations in the future (and before your local statute of limitations on tax fraud runs out). A few Caribbean islands have been much more cooperative with the U.S. in recent years. I'd be real careful about leaving money in the Caymans. While you're scamming your country, they may be scamming you! And you probably won't have a chance in their courts against a native or someone who is well connected.
There's plenty of info on the web about running a business offshore, but you can't trust anyone to tell you the truth. Best bet might be to find a sound local bank in India with a branch there.
Your situation may vary from the norm. People use offshore banks and businesses to hide assets from creditors and from spouses in divorce. Or in some cases to legitimately lower taxes. But the main reason is tax evasion or to hide stolen money.