You can send the context (Activity that controls the view) to the AsyncTask:
public class AsyncTask {
protected void execute(Context context, HashMap<String, String>... params) {
...
Then in the onPostExecute method of the AsyncTask, you can call a method of the activity to update the view.
@Override
protected void onPostExecute(HashMap<String, String> result) {
((MyActivity) context).updateView(result);
}