As a green card holder (with or without a reentry permit) you are a resident of a state or US territory (Puerto Rico, Virgin Islands, etc.) and must comply with the tax laws of your state or territory of residence, which for you is California.
That might include filing state taxes for non-US income. You'll have to consult a tax accountant and/or do your own research to find out. Each state has its own different tax rules. The California tax authorities probably have a web site where you can download some of the laws and forms.
Try not to work abroad too much longer, especially if it's a non-US company. Working abroad for long periods for a non-US company can cause you to lose your green card, even if you have a reentry permit.
PD: Jan 2003 (EB3 rest of world)
I-485 Approved: July 2007
I am a layman, not a lawyer. What I write here is not official or professional legal advice. In addition, my answers on this forum are specific to the scenarios discussed in each thread and should not be generalized to other situations.