User's homepage depending on their organic group
There is a module (Frontpage) that allows to set a different front page for anonymous users, and authenticated users. 

The module allows third-party modules to alter the page to which the users are instead redirected, or to alter the structure array used to render the page.

As alternative, you can create a custom module that, using code similar to the one used by Frontpage, redirect users to a specific page, basing on specific criteria.

The module should implement hook_menu() and associate a menu callback to, for example, http://example.com/frontpage; the page callback of that menu item should simply verify a condition is verified, and then redirect the users to a specific URL.

The code skeleton could be something similar to the following:

/**
 * Implements hook_menu().
 */
function mymodule_menu() {
  $items = array();

  $items['frontpage'] = array(
    'page callback' =&gt; 'mymodule_frontpage_view',
    'access arguments' =&gt; array('access content'),
    'type' =&gt; MENU_CALLBACK,
  );

  return $items;
}

function mymodule_frontpage_view() {
  // These variables can be useful to redirect the users
  // to specific pages, basing on the language currently set for
  // the content, or on the fact the user is logged in.
  $langcode = $GLOBALS['language_content']-&gt;language;
  $logged_in = user_is_logged_in();
  $usergroups = og_get_groups_by_user($user);
  $group = og_load($gid);
  $groupnode = $group-&gt;etid;
  $redirectpath = 'node/'.$groupnode-&gt;nid;
  drupal_goto($redirectpath);

}