Delta Air Lines bought a small stake in Korean Air Lines' parent company and said it wants to increase it to 10%, giving a boost to the management of South Korea's top carrier that seeks to thwart a local activist fund's challenge. Shares of the parent, Hanjin Kal Corp, tumbled 15% Friday, as Delta's move dashed investor hopes of a battle to control the family-run group that had driven up shares since the death of patriarch Cho Yang-ho in April. Korean Air, which has a joint venture with Delta since last year, said Friday it believes Delta's 4.3% stake buy intends to ensure the 'stable management" of the company and support for its leadership. Should Delta raise its stake to 10% in Hanjin Kal, the airline's founding family and its allies will have a total stake of 39%, versus the 16% stake held by the activist fund, KCGI. <br/>