[patio11]

to have the transaction go through on your site makes it feel more official

You tech people keep forgetting that reading a URL bar requires superpowers. I guaranteed you, having suffered many customer support incidents because of this: many people cannot tell the difference between getting redirected to Google/Paypal and the site they were originally on. (For that matter, a huge portion of my customers don't understand that I am not Yahoo or Internet Explorer.)

[pbz]

I agree with noticing the URL change, but what's a lot more noticeable is when the look of your site changes. They're used to your site's look and feel. When you direct them to a different site, even if it sort of looks like the original site, it's a big speed bump in the flow. Makes you stop and think (hey, what's going on?!) and question if you're in the right place (did I click the wrong button?!). You may even get suspicious and leave. You'd probably feel the same if at a supermarket when it's time to take out the card and pay, within seconds the building changes, the cashier is no longer there, the door you came through is gone, the lightning is different, the people who surrounded you disappeared; only the colors sort of look the same...

[detst]

In my experience, some level of similarity (colors) is all that really matters. People have no problem accepting that the shopping cart and check out experience might be a little different.

You may feel different about it but the average person doesn't.

[bergkampf]

Very William S. Burroughs.

[sachinag]

This is true. But it precludes you from doing two-click checkouts on the second transaction (wink wink) and real users really don't have a problem whipping out their credit cards on a new site.