You may travel abroad if you had applied for Green Card renewal and if the application is pending. While you file Green Card Renewal Form I-90, for Green Card renewal, USCIS will verify your application and attach a sticker to your Green Card. That Green Card with a sticker will serve as a proof of your status until you get a Green Card valid for ten years.
For more details about Green Card Renewal/renovación de green card, US citizenship and Immigration services please visit Immigration Direct a site that has empowered thousands of immigrants to successfully prepare their USCIS Forms such as EAD, citizenship test, I-9, I-485, h1b visa, deferred action, fiance visa, INS and many more.