Originally Posted by Majuki

Welcome to FlyerTalk! You will use your green card at the kiosks, so there is no problem there. Did you provide a US address or point of contact?

Here is a link to the frequently asked questions. The question titled "How will I receive my Global Entry card?" says that if you don't have a US address it will be mailed to a US point of contact or Global Entry enrollment center.

You could try calling the customer service number and see if they have the address where the card was mailed. Maybe it was mailed to the Doha enrollment center?

In the worst case, you can request a replacement card to a US address. There is a small fee to request a new card, but it's an option. The card will be helpful at some airports where the contract employees want proof of GE membership or if you're reentering the US by land from Mexico or Canada.