Help 1913 unit marked

[jayhawkhenry]

Hello all,

I have a 1913 DWM that has a 1920 reissue stamp. It is totally matched, all proofs are correct. The strap is marked, S.G.I.4 (which has been struck through) and then stamped S.Ka.I. 377

I have not been able to find anything that would fit. Any help would be great to ID the unit or organization.

Thanks in advance.
Henry