Automatic transition to new page in WPF Browser-style navigation model

Question

I am using WPF/C# with the browser-style navigation model.

At one point if the user presses a button, I will initiate a long-running task. At that point I'd like to display a progress bar and, when then long-running task completes, transition to another page, without user interaction.

Setting up the progress bar and keeping it updated seems fairly straightforward - I've done that in winforms apps. But initiating the page transition, while respecting restrictions on how threads interact with the GUI elements is more of a problem. I'm probably making a bigger deal of this that it really is (that'd be nice), but right now I'm stuck.

Thanks for any thoughts, pointers, random advice, etc.