Thanks Mike, the scale is a quarter of ring visible in the corner of the image, the fragments of it scattered all through in the rock, the wall has special structure, with a slit like division in the middle and minor partions prependicular to it on both sides of the division, probably as you suggest it belongs to a rudist bivalve.

it indeed looks more like fragments of thick shells than algae. Lithified algae occur as fragments only in high-energy sediments, is that the case ?

The problem regarding these specimen is they are found on transported (reworked) clast, with good roundness indicating long distance transportation, so it is not easy to confer the energy of system based on them, alone. However, all these clasts are bearing these (as you suggest shell like fragments), in scattered manner( probably indicating, origination from a reefal source). At first sight they seemed shell fragments to me,too, becuase of obvious curvature in all speciemen, but when I closely looked at the wall structure with my loop I found that it is not wall type of typical bivalves, but as Dr Simmons suggest they might belong to Rudist bivalves. In the case of Algae, I assumed they may belong to Corallinacean red algae group, however morphological evidences are more in favour of being a rudist bivalve.

If some colleagues are experts on rudist bivalve I would be thankful to have their confirmation.

thiis fragment of invertebrate fossil?but no algae fossil!

It does not look like algae, but If you have a thin section photo it may help better,

I agree with Dr.Ismail Omer Yilmaz if you have a thin section image (photomicrograph) of the wall structure that would be good.

Its like a bioclastic limestone