You can file the divorce petition in USA as you are a green card holder.
A green card holder identifies its holder as a U.S. permanent resident, with rights to enter, exit, work, and live in the United States for their entire life and hence they are governed under process of US laws.
Filing of a divorce petition in India does not prevent the other person from filing a divorce petition in USA. We are seeing people filing divorce petitions in USA soon after the spouse files in india and the speed at which divorce decrees are granted in USA are in fact bringing the parties to the negotiation table( as it involves green card, future citizenship and also alimony).
Also please note that the indian courts do not recognize the USA divorce decree, if the proceedings are ex-parte. Both the parties should have contested the divorce or given mutual consent divorce.
There is no arrangement wherein the USA Courts can transfer the divorce proceedings to india and vice versa.