You need to do this:
OleDbConnection connection = new OleDbConnection(
"Provider=Microsoft.ACE.OLEDB.12.0;Data Source=Inventar.accdb");
DataSet DS = new DataSet();
connection.Open();
string query =
@"SELECT tbl_Computer.*, tbl_Besitzer.*
FROM tbl_Computer
INNER JOIN tbl_Besitzer ON tbl_Computer.FK_Benutzer = tbl_Besitzer.ID
WHERE (((tbl_Besitzer.Vorname)='ma'))";
OleDbDataAdapter DBAdapter = new OleDbDataAdapter();
DBAdapter.SelectCommand = new OleDbCommand(query, connection);
DBAdapter.Fill(DS);
By the way, what is this DataSet1? This should be "DataSet".