Complete Transaction on 3rd Party Landing Page This post is outdated

Is it possible to complete a full transaction (including processing a credit card number) from a third party landing page? I've worked with the "Buy Button" to view / select items and generate a Checkout url, but in order to complete the full transaction the user needs to go to the checkout page, which takes them off the landing page.

I have seen documentation for processing a Transaction object (which has a "payment_details" attribute), but I'm not sure how to integrate that into the landing page flow. Any advice would be appreciated. Thanks!