We report on the results of deep narrow-band Ly \alpha and broad-band U and I imaging of the fields of two Gamma-Ray bursts at redshift z=2.04 ( GRB 000301C and GRB 000926 ) .
We find that the host galaxy of GRB 000926 is an extended ( more than 2 arcsec ) , strong Ly \alpha emitter with a rest-frame equivalent width of 71 ^ { +20 } _ { -15 } Å .
The galaxy consists of two main components and several fainter knots .
GRB 000926 occurred in the western component , whereas most of the Ly \alpha luminosity ( about 65 % ) originates in the eastern component .
Using archival HST images of the host galaxy we measure the spectral slopes ( f _ { \lambda } \propto \lambda ^ { \beta } ) of the two components to \beta = - 2.4 \pm 0.3 ( east ) and - 1.4 \pm 0.2 ( west ) .
This implies that both components contain at most small amounts of dust , consistent with the observed strong Ly \alpha emission .
The western component has a slightly redder V - I colour than the eastern component , suggesting the presence of at least some dust .
We do not detect the host galaxy of GRB 000301C in neither Ly \alpha emission nor in U and I broad-band images .
The strongest limit comes from combining the narrow and U-band imaging where we infer a limit of U ( AB ) > 27.7 ( 2 \sigma limit per arcsec ^ { 2 } ) .
The upper limits on the Ly \alpha flux implies a Ly \alpha equivalent width upper limit of \sim 150 Å .
We find eleven and eight other galaxies with excess emission in the narrow filter in the fields of GRB 000301C and GRB 000926 respectively .
These galaxies are candidate Ly \alpha emitting galaxies in the environment of the host galaxies .
Based on these detections we conclude that GRB 000926 occurred in one of the strongest centres of star formation within several Mpc , whereas GRB 000301C occurred in an intrinsically very faint galaxy far from being the strongest centre of star formation in its galactic environment .
Under the hypothesis that GRBs trace star formation , the wide range of GRB host galaxy luminosities implies a very steep faint end slope of the high redshift galaxy luminosity function .