Final answer:
After an asynchronous task, the onPostExecute() method is used to update the UI with results processed in the background thread.
Step-by-step explanation:
The method that is executed on the UI thread after the asynchronous thread has finished executing within a class for an asynchronous task is C. onPostExecute(). This method runs after the doInBackground() method has completed processing. It is used to update the user interface with the results from the background computation. Options A (doInBackground()) and D (onProgressUpdate()) are called during the asynchronous processing, and B (onPreExecute()) is called before the background task begins.