How to run something in the STA thread?

You can use the Dispatcher class to execute the method call on the UI-Thread. The Dispatcher provides the static property CurrentDispatcher to get the dispatcher of a thread.

If your object of the class, that creates the InkPresenter, is created on the UI-Thread, then the CurrentDispatcher method returns the Dispatcher of the UI-Thread.

On the Dispatcher you can call the BeginInvoke-method to call the specified delegate asynchronously on the thread.

You can start STA Threads like so:

    Thread thread = new Thread(MethodWhichRequiresSTA);
    thread.SetApartmentState(ApartmentState.STA); //Set the thread to STA
    thread.Start(); 
    thread.Join(); //Wait for the thread to end

The only problem is that your result object must be passed along somehow.. You can use a private field for that, or dive into passing along parameters into threads. Here I set the foo data in a private field and start up the STA Thread to mutate the inkpresenter!

private var foo;
public void SearchForFooCallbackMethod(IAsyncResult ar)
{
    foo = GetFooFromAsyncResult(ar); 
    Thread thread = new Thread(ProcessInkPresenter);
    thread.SetApartmentState(ApartmentState.STA);
    thread.Start();
    thread.Join(); 
}

private void ProcessInkPresenter()
{
    var inkPresenter = XamlReader.Parse(foo.Xaml) as InkPresenter;
}

Hope this helps!