You would have to report the income you earn from the business to the IRS. Green card holders are required to file tax returns for worldwide income.
There are tax treaties, deductions and credits you can use to reduce or eliminate the US taxation of foreign income, but you are still required to report the income. Make sure to hire a tax accountant or attorney to assist with your tax returns, otherwise you risk overpaying the taxes because you don't know how to make use of all the deductions and exemptions etc., or underpaying and being penalized by the IRS.