Pass count, limit and offset to navigation/pagination view. From there use the offset and limit in your custom query

yes :-)
thank you ismayil for your quick response
have a good time :-)

for elgg-novices I describe how I solve my problem:

on top I initialize the two variables:  
 
$limit = max ((int) get_input ("limit", 5), 0);
$offset = sanitise_int (get_input ("offset", 0), false);

// found in Jeroen Dalsem Profile Manager :-)


then I execute the sql statement:

$query = "SELECT elgg_entity_relationships.guid_one, elgg_entity_relationships.guid_two, SUBSTRING(relationship,22) AS group_guid

FROM elgg_entity_relationships

GROUP BY elgg_entity_relationships.guid_one, elgg_entity_relationships.relationship, SUBSTRING(relationship,22)

HAVING (((elgg_entity_relationships.relationship) Like 'group_certified_vote_%')) LIMIT " . $limit . " OFFSET " . $offset;

$result_recordsets = get_data ($query);   

and format the html-output

       

            foreach ($result_recordsets as $dataset) {

            content .= . . . .  .

. . . . .

then I count the recordsets for pagination

 $query = "SELECT COUNT( * ) as total FROM ( SELECT elgg_entity_relationships.guid_one FROM elgg_entity_relationships GROUP BY elgg_entity_relationships.guid_one, elgg_entity_relationships.relationship HAVING (((elgg_entity_relationships.relationship) LIKE 'group_certified_vote_%'))

) derivedTable";

$result =  get_data ($query);

$recordset_count = $result[0]->total;

then I add the pagination:

$content .= elgg_view ("navigation/pagination", array ("offset" => $offset, "limit" => $limit, "count" => $recordset_count));

and then I display the html in a group widget for instance:

                 echo elgg_view ('groups/profile/module', array (

                    'title' => elgg_echo ('audit:group module:group_auditors:certified'),

                    'content' => $content,

                    'all_link' => Null,

                    'add_link' => Null,

                ));


Note:

best practice is to use the functions:
elgg_list_entities_from_relationship ($options);
or
elgg_get_entities_from_relationship ($options);
with that functions pagination is much more easier :-)

but in my case I (mis)used the field "relationship" as a fourth filter of the relationship table
and I had to make the query with a LIKE clause

thanks again to Ismayil Khayredinov