Android : Where and how to do network call when using fragments

I am building an app that has fragments. Im not entirely sure when to make a http nw call to get data to populate components within these fragments. I have a call that gets all the data i need for all my fragments to draw the screen. I have tested that a async task gets that data ok but in the postExecute i don't have access to components unless im in the fragment class, even then how would i put it in there.

I can do a asyncTask and see my data coming back but where do i put this, i want to make the call once. ActivityTileData.getLoginTileDataArray(getActivity()); currently returns dummy data, ideally this would do the network call.

public class StaggeredGridActivityFragment extends FragmentActivity {

private static final String TAG = "StaggeredGridActivityFragment";
@Override
protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);

    this.requestWindowFeature(Window.FEATURE_NO_TITLE); //remove title bar

    final FragmentManager fm = getSupportFragmentManager();

    // Create the list fragment and add it as our sole content.
    if (fm.findFragmentById(android.R.id.content) == null) {
        final StaggeredGridFragment fragment = new StaggeredGridFragment();
        fm.beginTransaction().add(android.R.id.content, fragment).commit();
    }
}


private class StaggeredGridFragment extends Fragment implements
        AbsListView.OnScrollListener, AbsListView.OnItemClickListener {
            private StaggeredGridView mGridView;
            private boolean mHasRequestedMore;
            private TilesAdapter mAdapter;

            private ArrayList<String> mData;

            @Override
            public void onCreate(final Bundle savedInstanceState) {
                super.onCreate(savedInstanceState);
                setRetainInstance(true);
            }

            @Override
            public View onCreateView(final LayoutInflater inflater, final ViewGroup container, final Bundle savedInstanceState) {
                return inflater.inflate(R.layout.activity_sgv, container, false);
            }

            @Override
            public void onActivityCreated(final Bundle savedInstanceState) {


                //Encapsulate all within a post cereate from a async task or call a blocking http call
                super.onActivityCreated(savedInstanceState);

                mGridView = (StaggeredGridView) getView().findViewById(R.id.grid_view);

                if (savedInstanceState == null) {
                    final LayoutInflater layoutInflater = getActivity().getLayoutInflater();
                    View header = layoutInflater.inflate(R.layout.list_item_header_footer, null);
                    mGridView.addHeaderView(header);
                }

                if (mAdapter == null) {
                    mAdapter = new TilesAdapter(getActivity(), R.id.summary1_value);
                }

                if (mData == null) {
                    mData = ActivityTileData.getLoginTileDataArray(getActivity());
                }


                for (String data : mData) {
                    mAdapter.add(data); //Add each mData TileAdapter element to an mAdapter where it will be further broken down and used by the TileAdapter
                }

                mGridView.setAdapter(mAdapter);
                mGridView.setOnScrollListener(this);
                mGridView.setOnItemClickListener(this);
            }